The
making
of
an
Instrument
to
finde
out
the
situation
of
any
plat
or
Diall
,
and
to
place
them
already
prepared
.
CAP.
I.
FOr
asmuch
as
it
is
necessary
before
you
can
drawe
my
Dial
,
to
know
how
your
plat
is
already
or
ought
afterward
to
be
placed
,
it
shal
be
expedient
to
shew
the
making
and
vse
of
an
Instrument
,
whereby
you
may
examine
and
try
all
plain
plats
and
place
all
dials
being
ready
made
and
prepared
.
Prouide
therefore
an
halfe
circle
of
Peare-trée
,
Walnut-trée
,
Bor
,
or
any
other
close
grained
and
solide
wood
,
being
well
seasoned
,
so
that
the
alteration
of
the
weather
at
any
time
may
not
make
it
change
from
the
first
proportion
ther
of
.
Let
it
be
perfectly
tryed
on
both
sides
of
an
euen
thickenesse
,
halfe
or
thrée
quarters
of
an
inch
thick
or
more
if
you
will
,
and
sir
or
eight
inches
broad
as
you
thinke
good
.
The
edge
or
side
A.
B.
must
be
very
right
.
Then
draw
the
Line
C.
D.
thrée
quarters
of
an
inch
equally
distant
from
the
side
A.
B.
place
one
foot
of
your
compasses
in
the
centre
E.
which
is
the
midst
of
the
line
C.
D.
and
with
the
other
draw
halfe
a
circle
from
C.
to
A.
deuide
it
into
two
equall
partes
or
quadrants
,
and
laying
your
ruler
vpon
the
centre
E.
and
vpon
this
diuision
drawe
the
line
E.
F.
this
done
,
deuide
eche
of
these
quadrants
into
90.
equall
degrées
or
partes
,
which
you
may
thus
doe
:
First
,
deuide
eche
of
them
into
thrée
equall
partes
,
and
euery
of
these
into
thrée
other
partes
,
so
shall
you
haue
9.
diuisions
in
either
quadrant
,
whereof
euery
one
shal
represent
ten
degrées
.
Againe
,
part
euery
one
of
these
into
two
,
and
ech
of
those
into
fiue
(
if
you
can
)
and
so
is
eche
quadrant
diuided
into
90.
degrées
.
Moreouer
,
it
were
necessary
if
your
Instrument
were
large
inough
,
to
parte
ech
degrée
into
60.
minutes
,
or
at
the
least
into
3.
whereof
ech
parte
may
conteine
20.
minutes
.
This
done
,
fasten
a
thread
wel
wared
in
the
centre
E.
with
a
plommet
of
leade
on
the
end
,
so
that
it
may
moue
at
frée
libertie
.
You
may
also
(
if
you
will
)
vpon
this
side
of
the
quadrant
between
E.
D.
draw
the
diall
whose
delineation
is
taught
in
the
28.
Chapter
.
dialing diagram
It
were
necessary
to
have
here
a
little
hole
with
a
couer
to
put
in
your
pl●●●…et
&
thread
.
The
●omer
●●●
of
●●●●
Instrument
thus
finished
,
let
the
other
be
altogether
li●e
vnto
it
,
except
that
in
stead
of
the
the
thread
with
the
pl●●●●…t
,
you
must
haue
a
plombrule
made
in
this
maner
.
Prepare
a
péece
of
very
good
wood
,
try
it
perfectly
on
both
sides
to
an
equal
thicknes
,
let
it
be
about
half
an
inch
thick
,
and
twise
so
broad
as
the
space
betwéene
the
line
C.
D.
of
your
instrument
and
the
edge
A.
B.
in
the
midst
therof
draw
the
right
line
G.
H.
and
placing
one
foote
of
your
compasses
in
the
point
G.
with
the
other
make
a
halfe
circle
according
to
the
breadth
of
the
ruler
,
whereby
you
may
cut
the
end
round
,
make
the
other
end
with
a
sharp
point
right
in
the
end
of
the
line
G.
H.
as
you
sée
in
this
figure
.
Let
the
distance
betwéen
the
point
G.
and
the
end
H.
be
so
much
as
is
the
semidiameter
of
the
quadrant
,
make
by
G.
an
hole
so
great
that
a
plommet
of
lead
hanging
by
a
thread
from
the
sharpe
end
,
may
moue
therein
at
libertie
:
Make
also
an
other
round
or
square
hole
,
wherein
you
may
place
a
néedle
touched
with
the
Loadstone
,
as
in
the
compasses
or
dyals
you
sée
.
Finally
,
make
a
little
hole
in
the
point
or
centre
G.
and
with
a
broad
headed
na●e
of
brasse
fasten
it
vpon
the
centre
E.
of
your
Instrument
,
so
as
it
may
moue
&
turne
which
way
you
wil
,
and
then
your
Instrument
is
finished
.
Note
that
you
may
make
your
Instrument
in
forme
of
a
quadrangle
rightangled
,
as
Witekindus
teacheth
,
cutting
a
round
furrow
without
the
circle
and
degrées
made
,
for
the
plommet
to
hang
at
libertie
in
:
so
shall
you
néede
but
one
side
of
your
instrument
to
vse
,
with
a
compasse
or
needle
touched
with
the
Loadstone
for
declinations
.
But
the
form
of
the
other
,
whose
making
we
haue
taught
,
seemeth
more
commnodious
,
beholde
the
Figure
.
The
vse
of
this
instruement
.
CAP.
2.
dialing diagram
The
vse
of
this
instrument
is
in
examining
and
placing
the
plat
or
dial
.
In
immoueble
plats
,
to
know
how
they
stand
,
as
if
you
would
make
a
Diall
vpon
a
wall
,
first
you
must
vnderstand
whether
the
wall
be
erect
or
els
recline
or
incline
:
then
whether
it
be
direct
East
,
West
,
North
,
or
South
,
or
els
decline
,
which
you
cannot
know
without
the
helpe
of
this
Instrument
.
Againe
,
in
moueable
plats
for
the
placing
of
them
,
as
if
you
haue
made
a
South
diall
or
any
other
kinde
,
by
this
Instrument
you
shall
easily
and
perfectly
place
them
.
The
triall
of
a
plat
for
a
Horizontall
Diall
.
IF
your
plat
séeme
to
lye
plaine
,
making
no
angle
with
the
horizon
,
set
the
side
or
diameter
A.
B.
of
your
Instrument
vpon
it
,
and
erect
the
plombrule
right
vp
betwéene
the
two
quadrants
precisely
ouer
the
lyne
E.
F.
then
if
the
thread
with
the
plommet
hanging
at
liberty
fall
directly
vpon
his
line
G.
H.
which
way
soeuer
you
turne
your
Instrument
,
such
a
plat
is
saide
to
make
no
angle
with
the
horizon
:
and
therefore
the
diall
which
is
made
vpon
it
,
is
called
a
Horizontall
diall
.
In
like
maner
may
you
place
this
kinde
of
dial
being
ready
made
parallele
to
the
horizon
,
and
by
the
help
of
the
néedle
direct
the
stile
towards
the
North
pole
.
The
trying
of
plats
for
Erect
,
Direct
,
South
,
North
,
East
and
West
Dials
.
WHen
the
plat
standeth
vpright
,
it
maketh
a
right
angle
with
the
Horizon
,
and
is
called
Erect
,
whereof
some
beholde
one
priucipall
part
of
the
world
directly
as
the
South
,
North
,
East
,
or
West
:
other
decline
as
the
South
and
North
,
toward
the
East
or
West
,
of
which
kindes
hereafter
.
To
examine
an
Erect
plat
,
apply
the
side
or
diameter
A.
B.
of
your
Instrument
vnto
it
,
the
thread
with
the
plommet
on
the
foreside
hanging
at
liberty
.
If
the
thread
fal
vppon
the
line
E.
C.
or
E.
D.
the
plat
is
Erect
.
This
done
,
apply
the
said
line
or
diameter
A.
B.
to
the
plat
,
your
Instrument
being
placed
equally
distant
to
the
Horizon
,
and
the
plombrule
vpon
the
line
E.
I.
then
if
the
néedle
stand
directly
ouer
his
caracter
,
the
end
touched
with
the
Loadstone
being
next
to
the
plat
,
that
plat
is
called
a
South
Erect
Direct
.
In
the
North
all
the
foresaid
things
are
to
be
considered
,
except
onely
that
the
end
of
the
néedle
touched
with
the
loadstone
is
farthest
from
the
plat
.
These
things
knowen
,
you
may
easily
finde
out
the
East
and
West
Erect
Direct
,
if
either
you
haue
a
line
drawen
squire
wise
to
the
caracter
of
the
néedle
,
or
els
if
you
place
the
plombrule
ouer
the
line
E.
C.
or
E.
D.
And
here
note
,
that
the
East
and
West
,
are
not
saide
to
decline
,
because
the
declination
is
accounted
from
the
south
and
North
,
to
the
direct
East
,
and
West
pointes
.
The
examining
of
plats
for
Declining
Dials
.
ALl
such
plats
as
beholde
not
some
principall
part
of
the
world
directly
,
are
called
Declining
.
The
quantity
of
their
declination
is
found
out
thus
.
Apply
the
diameter
A.
B.
of
your
Instrument
to
the
plat
,
remembring
to
hold
it
equally
distant
from
the
Horizon
.
Then
moue
the
plombrule
vntill
the
néedle
standeth
right
ouer
the
caracter
,
and
the
point
of
the
ruler
,
which
toucheth
the
degrées
in
the
limb
,
shall
shew
how
many
degrées
and
minutes
it
doth
decline
:
either
toward
the
East
if
the
plumb-rule
lye
in
the
quadrant
C.
E.
F.
or
toward
the
west
,
if
in
the
quadrant
D.
E.
F.
The
trying
of
such
plats
as
recline
.
IF
the
plat
standeth
not
vpright
,
but
maketh
an
obtuse
or
blunt
angle
with
the
Horizon
,
it
is
saide
to
recline
.
The
degrées
of
reclination
are
found
out
thus
.
Apply
the
diameter
A.
B.
of
your
Instrument
to
the
plat
,
the
one
end
placed
vpward
,
the
other
downward
:
than
moue
the
plomrule
(
the
thread
with
the
plommet
hauing
frée
course
)
vntill
the
thread
hang
precisely
ouer
the
line
G.
H.
then
the
point
of
the
ruler
shall
shew
the
degrées
of
reclination
.
How
Inclining
plats
are
tried
.
BUt
if
the
angle
which
the
plat
maketh
with
the
Horizon
be
acute
or
sharpe
,
then
it
doth
incline
.
The
quantity
of
inclination
is
thus
knowen
.
Apply
the
diameter
A.
B.
of
your
instrument
to
the
plat
,
the
thread
with
the
plommet
of
the
former
side
hanging
at
liberty
,
and
mark
what
degrée
and
minute
the
thrad
shal
cut
,
for
so
much
is
the
inclination
.
The
manner
of
trying
those
plats
which
recline
and
decline
,
or
incline
and
decline
.
IF
your
plat
shall
both
recline
and
decline
,
or
incline
and
decline
:
First
séeke
out
the
reclination
as
hath
béen
shewed
,
and
then
the
declination
as
in
Erect
declining
.
The
making
of
a
Horizontall
,
or
plaine
lying
Sunne
Dial.
CAP.
3.
YOur
plat
being
prepared
smoothe
and
plaine
,
drawe
vpon
it
two
lines
,
as
in
the
figure
following
,
the
one
A.
B.
the
other
C.
D.
cutting
themselues
squirewise
,
that
is
,
making
right
angles
in
the
point
E.
vpon
which
make
the
quadrant
of
any
circle
from
the
line
E.
C.
to
the
line
E.
A.
or
E
B
and
write
at
C.
the
North
,
at
D.
the
South
,
at
A.
the
East
,
at
B.
the
West
.
And
the
line
C.
A.
which
here
is
the
quadrant
being
deuided
into
90.
degrées
or
parts
,
the
eleuation
of
the
Pole
shal
be
accounted
in
it
(
which
in
our
example
is
52.
d.
from
C.
to
A.
and
at
the
ende
of
this
number
drawe
a
line
from
the
centre
E.
which
shal
be
E
F
representing
the
stile
and
artrée
of
the
world
.
Then
draw
an
other
line
K.
L.
by
C.
or
by
some
other
point
of
the
line
D.
C.
squire
wise
,
so
long
as
you
can
which
shal
be
called
the
touch
line
,
or
line
of
Contingence
.
Then
measuring
with
your
compasses
the
least
distance
of
the
point
O.
and
the
line
E.
F.
or
the
Stile
,
the
one
foot
placed
in
O.
which
is
the
point
of
intersection
,
and
the
other
extended
toward
E.
where
it
shal
chaunce
to
diuide
or
be
placed
in
the
line
E.
C.
marke
that
point
or
centre
with
the
letter
G.
and
draw
with
your
compasses
a
halfe
circle
vpon
this
centre
for
the
equinoctial
circle
,
from
H.
by
C.
to
I.
whose
diameter
must
be
equally
distant
to
the
line
L.
K.
Then
diuide
this
halfe
circle
into
12.
equall
parts
:
this
done
,
lay
a
ruler
vpon
the
centre
G.
and
vpon
euery
marke
or
diuision
made
in
the
halfe
Equator
,
and
where
the
ruler
shal
touch
the
line
of
contingence
,
there
make
marks
or
pricks
,
by
which
pricks
draw
lines
from
E.
for
the
houres
.
E.
C.
is
the
12.
houre
,
E.
B.
the
6.
in
the
morning
,
E.
A.
the
6.
at
euening
,
the
rest
you
may
sée
in
the
figure
.
And
whereas
in
Sommer
the
4.
and
5.
in
the
morning
,
and
also
the
7.
and
8.
at
euening
,
shal
be
necessary
in
this
kinde
of
Diall
:
prolong
or
draw
the
lines
of
4.
and
5.
at
euening
,
beyond
the
centre
E.
which
shall
shew
the
houres
of
4.
and
5.
in
the
morning
.
And
likewise
the
7.
and
8.
in
the
morning
,
for
the
7.
and
8.
at
euening
.
You
may
obserue
an
order
both
in
these
and
in
all
other
erect
direct
dials
,
by
diuiding
the
one
halfe
of
the
Equator
,
drawing
houre
lines
for
the
forenone
,
and
obseruing
the
same
distance
from
the
meridian
line
,
on
the
other
side
for
the
afternoone
:
for
the
line
of
the
11.
houre
in
the
forenoone
is
of
like
distance
from
the
Meridian
,
that
the
1.
is
in
the
afternoone
,
and
the
10.
as
2.
and
so
of
the
rest
.
When
you
would
draw
or
make
the
halfe
houres
,
you
must
diuide
euery
parte
of
the
Equator
into
2.
equall
parts
,
〈◊〉
the
ruler
and
the
line
of
contingence
as
you
find
in
the
drawing
of
the
houre
lines
.
And
this
remember
for
the
drawing
of
the
halfe
houre-lines
,
not
onely
in
this
kinde
,
but
also
in
all
other
kindes
of
dials
,
which
afterward
shall
follow
.
The
Stile
must
be
fixed
in
the
centre
E.
hanging
directly
ouer
the
Meridian
line
E.
C.
with
so
great
an
angle
,
as
the
lines
C.
E.
F.
make
,
declining
from
that
on
neither
sides
.
The
Equinoctiall
circle
,
the
Quadrant
,
the
line
of
the
Stile
and
of
Contingence
,
must
be
lightly
drawen
,
because
they
ought
to
be
put
out
againe
,
in
that
they
serue
to
no
vse
but
for
the
drawing
of
the
Diall
.
And
this
likewise
remember
in
all
other
kindes
of
Dials
,
that
the
preparatiue
or
pricked
lines
must
after
the
making
of
the
Dial
be
omitted
and
extinguished
,
as
altogither
vnprofitable
.
This
and
all
other
kindes
of
Dials
may
most
fitly
be
drawen
vpon
a
clean
paper
,
and
then
with
the
help
of
your
compasses
placed
on
the
plat
.
dialing diagram
The
making
of
a
South
Erect
,
direct
Diall
.
CAP.
4.
THe
making
of
this
,
is
almost
altogether
like
vnto
other
before
.
Draw
here
also
a
line
A.
B.
parallel
to
the
Horizon
,
out
of
the
middest
wherof
,
let
the
line
C.
D.
perpendiculer
to
that
be
extended
:
and
let
the
Quadrant
be
drawen
from
A.
to
D.
or
B.
to
D.
parted
into
90.
degrées
,
as
before
.
Aboue
C.
let
Zenith
be
written
,
beneath
D.
Nadir
;
nigh
vnto
B.
the
East
,
and
by
A.
the
West
.
In
the
Quadrant
number
the
Eleuation
of
the
Pole
(
which
in
our
example
is
52.
degrées
)
from
A.
toward
D.
And
at
the
end
hereof
draw
from
the
centre
C.
the
line
C.
E.
representing
the
Stile
:
and
by
D.
draw
the
line
of
Contingence
,
I.
K.
squirewise
,
as
before
.
Then
the
least
distance
of
the
point
or
intersection
D.
and
the
Stile
being
taken
with
your
Compasses
,
extend
th●n
in
the
line
D.
C.
the
one
foote
placed
in
D.
set
the
other
in
F.
toward
C.
and
draw
by
F.
the
Diameter
of
the
halfe
circle
of
the
Equator
equally
distant
to
the
line
K.
L.
which
must
be
made
vpon
the
centre
F.
from
G.
by
D.
to
H.
and
diuide
it
into
12.
equall
partes
,
vpon
euery
one
of
which
and
the
centre
F.
the
ruler
being
placed
,
whersoeuer
it
shal
happen
to
touch
the
line
of
contingence
,
there
make
markes
.
Then
from
the
centre
C.
by
these
marks
the
houre
lines
must
be
drawen
.
The
line
C.
A.
shall
shew
the
6.
in
the
morning
,
C.
B.
the
6.
at
euening
,
C.
D.
the
12.
&c.
The
Stile
must
be
placed
or
fixed
in
the
centre
C.
hanging
precisely
ouer
the
line
of
the
12.
houre
,
with
so
great
a
distance
,
as
the
angle
D.
C.
E
,
is
.
This
kinde
of
Dial
doth
receiue
and
shew
onely
but
12.
houres
at
the
most
.
dialing diagram
The
making
of
a
North
Erect
,
Direct
Diall
.
CAP.
5.
HEre
as
in
the
South
make
a
line
Parallele
to
the
Horizon
,
A.
B.
cut
it
squire
wise
with
the
Perpendicular
C.
D.
let
C.
be
the
centre
.
At
C.
write
Zenith
,
at
D.
Nadir
,
●c
.
From
C.
draw
the
Quadrant
of
a
circle
to
D.
or
B.
deuide
this
into
90.
Degrées
,
account
the
Eleuation
of
the
pole
(
which
in
our
example
is
52.
d
)
from
A.
toward
C.
Draw
at
the
end
of
of
this
number
the
line
E.
F
for
the
Stile
.
Afterward
draw
the
line
of
Contingence
by
C.
squire-wise
,
and
take
the
shortest
distance
,
with
your
compasses
betwéene
the
poynt
C.
and
the
Stile
,
placing
the
one
foote
in
the
point
C.
extend
the
other
toward
E.
in
the
line
C.
D
:
making
a
poynt
or
pricke
G
:
wherupon
(
as
a
centre
)
the
same
widenesse
of
the
compasses
remaining
,
describe
the
halfe
Equator
by
C.
ended
with
the
Diameter
H.
I.
equidistant
to
the
line
of
Contingence
.
When
you
haue
deuided
thus
halfe
circle
of
the
Equator
into
twelue
equall
partes
,
lay
the
ruler
vpon
the
centre
G.
and
vpon
each
diuision
of
the
Equator
,
and
where
it
shall
touch
the
Contingent
line
,
make
markes
.
This
done
,
draw
the
lines
for
the
houres
,
by
those
markes
from
the
centre
E.
but
those
very
fewe
,
that
is
,
two
nigh
vnto
A.
and
two
by
B.
but
prolong
and
extend
them
beyond
the
centre
E.
so
that
their
contraries
may
bée
made
:
for
in
this
kinde
of
Dials
there
bée
but
onely
ten
houres
profitable
,
that
is
,
4
,
5
,
6
,
7
,
8
,
before
noone
,
and
4
,
5
,
6
,
7
,
8
,
after
noone
;
which
shew
but
only
in
Sommer
,
from
the
entring
of
the
Sunne
into
♈
,
vntill
such
t●ne
as
it
entreth
♎
.
The
Stile
must
bée
fixed
in
the
centre
E.
placed
vpward
,
directly
ouer
the
lint
E.
C.
with
so
great
an
angle
as
I.
E.
C.
is
.
Let
the
line
C.
D.
bée
placed
vpward
perpendicularly
,
but
so
that
it
may
not
bée
almost
séene
,
as
afterward
seruing
to
no
vse
,
because
it
is
onely
a
line
preparatiue
.
Beholde
the
Figure
.
A
North
Diall
erect
,
direct
.
dialing diagram
The
making
of
the
East
and
West
Erect
Dials
.
CHAP.
6.
IF
you
know
the
making
of
one
of
these
,
you
may
easily
make
them
both
,
for
they
be
very
like
,
differing
onely
in
the
naming
of
the
houres
,
for
the
one
containeth
houres
for
the
forenoone
,
and
the
other
for
the
afternoone
.
You
must
therefore
on
your
plat
make
the
quadrant
of
a
circle
A.
B.
C.
which
may
afterward
easilie
bée
put
out
,
as
all
the
other
lines
must
bée
,
except
the
houre
lines
:
let
the
side
A.
B.
be
Perpendiculare
:
B.
C.
Parallele
to
the
horizon
,
and
let
the
arke
beholde
the
South
,
which
being
diuided
into
90.
degrées
,
nomber
therin
the
elenation
of
the
Pole
dounward
from
A.
toward
C.
by
the
end
of
this
number
,
and
by
the
Centre
B
,
draw
a
line
so
long
as
your
plat
will
giue
you
leaue
,
whose
South
ende
shall
behold
precisely
the
Equinoctiall
circle
.
At
which
end
draw
a
circle
whose
diameter
shall
bee
almost
the
third
part
of
the
line
.
Then
draw
another
diameter
or
line
in
the
centre
,
squire
wise
to
the
other
,
which
shall
shew
the
axtrée
of
the
world
,
and
be
the
line
for
the
6.
hour
.
After
ward
at
the
cutward
sides
of
the
circle
,
draw
two
contingent
lines
,
one
beneath
,
the
other
aboue
,
so
that
they
may
be
Parallele
to
the
middle
line
.
Deuide
each
quarter
of
the
circle
into
sixe
equal
partes
.
Then
place
the
ruler
vpon
the
centre
,
and
eache
of
those
markes
or
partes
,
and
where
it
toucheth
the
lines
of
contingence
there
make
markes
in
them
.
Afterward
draw
a
line
by
those
two
markes
which
be
next
to
the
6.
houre
,
in
the
lines
of
contingence
,
which
may
be
equallie
distant
from
the
line
of
the
6.
houre
.
In
like
maner
doe
with
the
rest
;
so
that
you
may
haue
in
the
East
Diall
,
two
aboue
the
6.
houre
,
the
4.
and
5.
in
the
morning
,
and
vnder
it
7
,
8
,
9
,
10
,
11.
In
the
West
Diall
like
wise
7.
and
8.
in
the
euening
aboue
the
6.
houre
,
and
vnder
it
6
,
5
,
4
,
3
,
2
,
1.
Neither
of
them
doe
shew
the
12.
houre
,
because
at
that
time
the
Sunne
beames
be
Parallele
to
the
plat
.
Fixe
the
Stile
in
the
centre
of
the
circle
right
vp
from
the
Plat
,
so
long
as
the
Semidiameter
of
the
circle
is
:
only
shewing
the
houre
with
the
very
top
or
end
thereof
.
Yet
it
were
more
conuenient
to
haue
it
placed
along
ouer
the
line
of
the
6.
houre
,
being
a
plate
of
yron
or
some
other
metall
,
being
so
broad
as
the
Semidiamer
of
the
circle
is
.
Behold
the
figures
folowing
.
The
East
diall
Erect
.
dialing diagram
The
West
Diall
erect
.
dialing diagram
Note
that
these
fiue
kinds
of
Dials
before
taught
may
be
made
vpon
a
stone
cut
square
in
forme
of
a
die
.
The
making
of
a
South
Erect
declining
Diall
,
which
may
be
placed
on
any
vpright
wall
whatsoeuer
.
CAP.
7.
IN
all
Declining
Dials
because
the
Stile
doth
not
hang
directly
ouer
the
meridianline
,
therefore
you
must
first
finde
out
and
place
the
Substile
(
which
is
the
line
ouer
which
the
Stile
directly
hangeth
)
and
lik
wise
the
line
of
the
Stile
:
which
may
bée
both
eastly
and
spéedily
performed
in
this
maner
.
First
,
by
your
instrument
séeke
out
the
Declination
of
the
wall
or
plat
,
whereupon
you
would
make
a
diall
,
which
for
example
suppose
I
had
found
to
be
50.
degrées
.
●
Therefore
drawe
the
Horizontall
line
A.
B.
let
the
Meridian
C.
D.
cut
it
squire
wise
in
the
point
E.
which
may
be
in
any
place
of
the
line
A.
B.
and
let
the
line
F.
G.
cut
the
meridian
squire-wise
in
the
point
C.
which
you
may
like
wise
take
in
what
parte
of
the
Meridian
you
thinke
most
conuenient
.
Upon
the
center
E.
describe
the
quadrant
of
a
circle
from
C.
to
A.
if
the
declination
of
your
plat
be
West-ward
,
or
from
C.
toward
B.
if
East-ward
(
as
in
this
example
it
is
)
diuide
it
into
90.
degrées
and
number
in
it
from
C.
toward
B.
the
Eleuation
of
the
Equator
38.
degrées
,
and
laying
your
ruler
[
](A00538-e3940-b)*
*
This
is
alwaies
so
much
as
the
Eleuation
of
the
Pole
,
wanteth
of
90.
degrees
.
vpon
the
center
E.
and
vpon
the
end
of
this
number
draw
the
line
E.
H.
Againe
account
in
the
quadrant
from
C.
toward
B.
the
declination
of
the
plat
being
50.
degrées
,
and
draw
the
line
of
Declination
E.
I.
from
E.
to
the
end
of
this
number
.
Then
take
your
compasses
,
set
one
foote
in
the
point
C.
extend
the
other
vnto
H.
(
which
is
the
intersection
point
of
the
line
E.
H.
with
the
line
C.
G.
)
and
that
same
widnesse
remayning
,
place
one
foote
in
the
centre
E.
and
with
the
other
marke
the
point
1.
in
the
line
E
I.
and
from
the
point
I.
draw
the
line
I.
K.
squire-wise
to
the
Meridian
E.
C.
placing
K.
at
the
intersection
it
maketh
with
E.
C.
Moreouer
take
with
your
compasses
the
iust
length
of
the
line
I.
K.
and
placing
one
foote
in
C.
turne
the
other
toward
F.
and
make
the
point
L.
in
the
line
C.
F.
drawe
the
Substile
from
E.
by
L.
Let
the
line
of
Contingence
bée
drawne
squire-wise
to
the
Substile
in
the
point
L.
This
done
,
take
the
distance
betwéene
the
centre
E.
and
the
point
K.
and
place
it
in
this
line
of
Contingence
from
the
point
L.
vnto
M.
and
make
the
point
M.
that
the
line
E.
M.
may
be
made
from
E.
vnto
M.
for
the
stile
.
Measure
with
your
compasses
the
least
distance
betwéene
the
point
L.
and
the
Stile
,
and
with
the
same
widenes
,
one
foote
remaining
in
L.
turne
the
other
toward
E.
and
make
the
centre
O.
in
the
Substile
:
vpon
which
describe
the
Equinoctiall
circle
.
Then
placing
your
ruler
vpon
O.
being
the
centre
of
the
Equinoctiall
circle
,
and
N.
(
which
is
the
point
of
intersection
of
the
Meridian
and
Contingent
)
marking
where
it
cutteth
the
circumference
,
for
there
you
must
begin
to
diuide
it
into
24.
equall
partes
,
not
withstanding
those
12.
are
onely
in
vse
which
are
next
the
contingent
.
Finally
,
place
your
ruler
vpon
the
centre
O.
and
vpon
the
seuerall
diuision
points
of
the
Equator
,
and
where
it
toucheth
the
line
of
Contingence
make
markes
,
by
which
from
the
center
E.
draw
the
houre
lines
.
Place
the
Meridian
perpendicularly
vpon
the
wall
,
the
centre
E.
vpward
,
the
Stile
pointing
downeward
.
Let
the
Stile
hang
directly
ouer
the
Substile
making
an
angle
equall
to
E.
M.
L.
The
making
of
a
North
Erect
Declining
Diall
.
CAP.
8.
THe
North
Erect
declining
Dial
differeth
from
the
South
onely
herein
,
that
the
centre
is
to
be
placed
downeward
,
the
Stile
pointing
vpward
to
the
North
Pole
,
and
that
the
Meridian
representeth
the
12.
houre
at
midnight
and
not
at
noone
.
Therefore
if
the
declination
bée
toward
the
East
,
you
must
account
the
houre
lines
from
that
which
is
as
it
were
the
Meridian
forthward
1
,
2
,
3
,
4
,
5
,
6
&c.
But
if
it
decline
toward
the
West
,
number
them
backeward
,
11
,
10
,
9
,
8
,
&c.
omitting
the
first
3.
which
are
before
Sunne
rising
and
after
Sunne
setting
in
our
eleuation
.
Let
the
line
E.
D.
bée
placed
perpendicularly
vpon
the
plat
,
and
the
Stile
point
vpward
to
the
North
Pole
.
Compare
this
figure
with
the
former
.
Another
way
to
make
the
South
Erect
Declining
Diall
.
CAP.
9.
ALbeit
we
haue
plainely
and
perfectly
shewed
the
making
of
the
South
and
North
erect
Declining
Dials
,
in
the
two
former
Chapters
;
yet
to
satisfie
them
that
delight
in
variety
;
here
is
also
declared
another
way
,
whereby
you
may
make
them
,
namely
,
by
the
helpe
of
Arithmetick
,
and
the
Table
of
Sines
which
is
Read
the
●se
of
the
Table
of
Sines
.
placed
in
the
end
of
this
booke
for
this
intent
.
Therefore
the
Eleuation
of
the
Pole
being
knowen
,
and
the
Declination
of
your
plat
,
by
your
Instrument
found
out
:
Multiply
the
Sine
of
the
complement
of
the
Eleuation
,
by
the
Sine
of
the
complement
of
the
Declination
,
diuide
the
product
by
the
whole
Sine
(
which
is
100000
)
and
you
shall
haue
a
quotient
Sine
,
whose
arke
is
the
distance
of
the
Stile
from
the
Substile
,
which
distance
kéep
.
Then
take
the
complement
of
this
distance
,
and
the
Elenation
of
the
Pole
,
and
multiply
the
Sine
of
the
lesser
by
the
whole
Sine
,
parting
the
product
by
the
Sine
of
the
greater
:
the
quotient
Sine
which
shall
come
of
this
diuision
,
shall
giue
you
an
Arke
,
whose
complement
is
the
distance
of
the
line
of
the
Substile
from
the
Meridian
,
which
distance
you
shall
likewise
kéepe
.
For
better
instruction
herein
,
consider
the
example
.
Example
of
a
South
Diall
declining
45.
d.
Eleuation
of
the
Pole
.
52.
d.
FIrst
I
enter
the
Table
of
Sines
,
for
the
Sine
of
the
complement
of
the
Eleuation
,
which
is
38.
d.
and
I
finde
it
to
be
61566.
Then
I
looke
for
the
Sine
of
the
complement
of
the
Declination
,
which
is
45.
d.
and
I
finde
that
to
be
70710.
This
done
,
I
multiply
the
one
by
the
other
,
and
the
product
is
435333
1860.
which
I
diuide
by
the
whole
Sine
being
100000
wherof
commeth
a
quotient
43533.
With
this
quotient
Sine
I
enter
the
Table
,
and
because
I
finde
not
the
iust
number
,
I
take
that
which
is
next
either
greater
or
lesse
vnto
it
:
(
which
you
must
alwaies
remember
to
doe
)
for
so
small
a
difference
maketh
no
alteration
,
and
therfore
I
take
in
stead
thereof
43523.
whose
Arke
is
25
d.
48.
m.
which
is
the
distance
of
the
Stile
from
the
substile
.
Then
I
take
the
complement
of
this
distance
,
which
is
64.
d.
12.
m.
whose
Sine
is
90031.
and
the
Eleuation
of
the
Pole
52.
d.
whose
Sine
is
78801.
and
multiplying
the
Sine
of
the
lesser
,
(
which
is
the
Eleuation
of
the
Pole
)
by
the
whole
,
100000.
the
product
is
7880100000.
which
I
diuide
by
the
Sine
of
the
greater
,
to
wit
,
the
Sine
of
the
complement
of
the
distance
of
the
Stile
from
the
Substile
,
whose
Sine
is
90031
,
whereof
commeth
this
quotient
87526
whose
Arke
is
61.
d.
5.
m.
The
complement
of
which
arke
is
28.
d.
55.
m.
being
the
distance
of
the
substile
from
the
Meridian
.
These
distances
being
thus
found
out
,
the
drawing
of
the
diall
foloweth
.
First
draw
a
line
Parallele
to
the
Horizon
A.
B.
out
of
whose
middle
point
C.
draw
the
Meridian
line
squire
wise
C.
D.
vpon
the
centre
C.
make
the
quadrant
of
a
circle
betwéene
A.
and
D.
Here
vnderstand
that
generally
in
all
kindes
of
declining
Dials
,
if
the
declination
be
towards
the
East
,
you
must
draw
the
quadrant
towards
the
West
,
(
except
in
the
South
reclining
declining
,
and
the
North
inclining
Declining
,
where
the
contrary
is
prescribed
)
But
if
the
declination
be
Westward
,
the
quadrant
must
be
drawen
Eastward
.
Hereby
you
shall
easily
know
on
which
side
you
ought
alwaies
to
draw
the
quadrant
,
and
which
way
the
figures
following
doe
decline
.
Your
quadrant
being
made
,
diuide
it
into
90.
degrées
:
number
therein
from
D.
the
distance
of
the
Substile
from
the
Meridian
,
(
which
is
28.
d.
55.
m.
Draw
at
the
end
of
this
number
the
line
C.
E.
for
the
Substile
.
Then
from
E.
towards
A.
account
the
distance
of
the
Stile
from
the
Substile
,
which
is
25.
d
48.
m.
and
at
the
end
hereof
,
draw
the
line
C.
F.
for
the
Stile
.
Afterward
by
the
point
E.
or
in
any
place
of
the
Substile
draw
the
Contingent
line
G.
H.
so
long
as
you
can
squirewise
to
the
Substile
.
Then
take
with
your
compasses
the
least
distance
betwéene
E.
and
the
Stile
,
the
one
foote
remaining
in
E.
and
the
other
extended
in
the
Substile
toward
C.
place
at
the
pricke
there
made
with
the
compasses
,
I.
vpon
which
pricke
as
a
centre
,
the
same
widenes
of
your
compasses
remaining
,
draw
a
circle
by
E.
which
shall
represent
the
equinoctiall
or
Equator
.
Then
lay
the
ruler
vpon
the
point
I.
and
the
intersection
(
whose
marke
is
K.
)
of
the
line
of
Contingence
and
the
line
C.
D.
which
is
alwaies
drawen
so
that
it
may
cut
the
other
)
and
where
the
ruler
so
placed
shall
touch
the
circle
,
there
make
a
marke
,
and
there
begin
to
diuide
it
into
24.
equall
partes
:
notwithstanding
those
12.
onely
are
to
be
vsed
,
which
doe
beholde
the
contingent
line
.
Then
lay
the
ruler
vpon
the
centre
I.
and
the
Contingent
line
by
euery
diuision
of
the
Equator
,
and
where
it
shall
touch
the
line
of
Contingence
,
there
make
markes
,
by
the
which
from
the
centre
C.
draw
lines
for
the
houres
,
so
many
as
shal
be
necessary
.
The
line
C.
D.
shall
alwaies
shew
the
12.
houre
,
which
must
hang
perpendicularly
.
Number
the
residue
of
the
lines
in
their
place
,
as
they
follow
in
order
.
The
line
A.
B.
in
such
as
doe
decline
is
vnprofitable
,
except
it
so
chance
that
some
houre
line
falleth
in
it
.
Let
the
Stile
be
fixed
in
C.
hanging
directly
ouer
the
Substile
,
with
so
great
an
angle
,
as
E.
C.
F.
is
,
declining
on
neither
side
.
Note
diligently
the
making
of
this
declining
Diall
,
because
in
those
which
follow
,
we
meane
not
to
repeate
those
things
which
héere
haue
béen
taught
.
And
this
one
kinde
well
knowen
,
all
the
other
will
séeme
most
easie
.
For
better
vnderstanding
hereof
beholde
the
figure
.
A
South
Erect
declining
Diall
.
dialing diagram
The
making
of
a
North
Erect
declining
Diall
another
way
.
CAP.
10.
THe
distance
of
the
Stile
from
the
Substile
,
and
of
the
Substile
from
the
Meridian
,
is
found
out
altogether
like
to
the
South
Erect
declining
.
Therefore
you
may
resort
thither
for
the
working
hereof
,
I
will
onely
drawe
the
Figure
.
Let
the
line
A.
B.
being
parallele
to
the
Horizon
,
cut
C.
D.
squire
wise
,
placing
E.
at
the
intersection
Draw
the
quadrant
from
C.
to
B.
diuide
it
into
90.ᵈ.
accounting
therein
from
C.
toward
B.
the
distance
of
the
Substile
from
the
line
,
which
is
(
as
it
were
)
the
Meridian
,
which
distance
is
28.ᵈ.
At
the
end
of
this
number
draw
the
line
E.
F.
for
the
Substile
.
Then
number
from
that
line
the
distance
of
the
Substile
and
the
Stile
,
which
is
25.
degrées
,
48
minutes
toward
B.
Draw
likewise
at
the
end
of
this
number
the
line
for
the
Stile
E.
G.
This
done
,
let
the
line
of
Contingence
be
drawen
squire
wise
by
the
point
F.
and
then
taking
the
least
distance
betwéene
the
point
F.
and
the
Stile
,
extend
the
compasses
in
the
line
F.
E.
the
one
foote
being
placed
in
F.
where
the
other
shall
deuide
the
line
,
place
the
letter
H.
With
the
same
widenes
of
the
compasses
draw
vpon
the
centre
H.
the
Equator
,
and
where
the
ruler
shall
touch
the
same
,
being
laid
vpon
the
centre
H.
and
the
intersection
of
the
Contingent
line
,
and
that
which
is
(
as
it
were
)
the
Meridian
,
begin
to
deuide
it
into
24.
equall
partes
.
Finish
all
things
remaining
,
as
in
the
South
erect
declining
,
onely
this
excepted
,
the
Stile
being
fixed
in
the
centre
E.
must
be
placed
vpward
,
beholding
the
substile
with
so
great
a
distance
or
angle
,
as
the
letters
F.
E.
G.
do
shew
.
The
line
C.
D.
being
applyed
to
the
plat
perpendicularly
,
sheweth
as
it
were
the
12.
houre
at
midnight
:
therefore
account
from
that
the
houre
lines
,
as
they
follow
in
order
,
1
,
2
,
3.
which
houres
haue
no
vse
in
this
kinde
of
Diall
for
our
Eleuation
,
but
from
4.
&c.
Let
the
line
A.
B.
be
parallel
to
the
Horizon
,
being
lightly
drawen
,
as
the
other
preparatiue
lines
be
,
seruing
afterward
to
no
vse
.
Note
,
if
the
plat
decline
towards
the
East
,
as
this
figure
doth
,
it
is
for
the
forenoone
:
and
you
must
account
the
houre
lines
from
that
which
is
(
as
it
were
)
the
Meridian
,
forward
4
,
5
,
6.
&c.
If
it
decline
toward
the
West
,
account
them
backward
11
,
10
,
9.
as
we
shewed
before
.
A
North
erect
declining
Diall
.
dialing diagram
The
making
of
a
Meridionall
or
South
Reclining
direct
Diall
.
CAP.
11.
IF
the
Reclination
of
the
plat
be
lesse
then
the
complement
of
the
Eleuation
of
the
Pole
,
adde
this
complement
,
and
the
Reclination
of
the
plat
together
,
and
with
this
number
as
if
it
were
the
Eleuation
of
the
Pole
make
a
South
erect
direct
diall
,
and
it
will
be
perfect
and
fit
for
your
plat
.
Example
and
delineation
of
a
South
Diall
,
reclining
25.
d.
MAke
the
first
line
A.
B.
drawe
also
an
other
C.
D.
cutting
the
other
with
right
angles
.
Then
adde
the
Complement
of
the
eleuation
of
the
Pole
(
which
is
25.
,
)
to
the
reclination
of
the
plat
(
which
is
38.ᵈ.
)
and
the
totall
summe
shal
be
63.ᵈ.
which
number
being
in
place
of
the
Eleuation
of
the
Pole
,
account
it
in
the
Quadrant
from
A.
towards
D.
and
at
the
end
hereof
,
draw
the
line
F.
for
the
Stile
.
Then
make
the
line
of
Contingence
K
L.
squire
wise
to
the
line
C.
D.
Afterward
take
the
least
distance
with
your
compasses
betwéen
the
point
G.
and
the
Stile
,
with
the
widenes
,
the
one
foote
extended
toward
C.
make
a
point
or
prick
E.
by
which
point
draw
the
line
H.
I.
equidistant
from
A.
B.
or
K.
L.
vpon
E.
make
a
halfe
circle
from
H.
by
G.
to
I.
which
being
diuided
into
12.
parts
,
finish
the
rest
as
the
South
Erect
direct
.
A
South
Direct
reclining
25.
d.
dialing diagram
BUt
if
the
Reclination
be
equall
to
the
complement
of
the
Pole
,
make
your
Diall
on
this
maner
,
like
to
the
East
and
West
.
Draw
a
line
Parallele
to
the
Horizon
A.
B.
so
long
as
the
plat
will
giue
you
leaue
,
diuide
it
into
7.
equall
parts
,
and
with
the
same
widenes
of
the
compasses
,
in
the
midst
of
the
line
,
make
a
circle
representing
the
Equator
.
Then
drawe
two
lines
of
Contingence
by
the
circumference
of
the
circle
,
equidistant
from
the
first
A.
B.
Diuide
the
Equator
into
24.
equall
parts
.
Finish
the
rest
like
the
East
or
West
diall
:
except
in
naming
the
houres
,
for
that
which
is
in
them
the
6.
houre
line
,
is
here
the
12.
&c.
A
South
Direct
reclining
38.
d.
dialing diagram
BUt
if
the
reclination
of
the
plat
be
greater
then
the
complement
of
the
Eleuation
of
the
Pole
,
substract
the
complement
of
this
Eleuation
out
of
the
reclination
,
and
that
which
remaineth
shall
serue
in
stead
of
the
Eleuation
of
the
Pole
:
with
which
Eleuation
make
your
diall
altogether
like
a
Horizontall
,
which
you
shall
finde
fit
for
your
plat
.
Example
of
a
South
Diall
,
reclining
55.
d.
FIrst
I
take
the
complement
of
the
Eleuation
,
which
is
38.ᵈ.
out
of
the
Reclination
of
the
plat
,
which
is
55.ᵈ.
and
there
remaineth
17.ᵈ.
which
number
kéep
for
the
Eleuation
of
the
Pole
.
In
Delineation
of
this
Diall
,
drawe
a
line
Parallele
to
the
horizon
A.
B.
draw
another
C.
D.
making
right
angles
with
the
line
A.
B.
Then
make
the
quadrant
from
A.
to
D.
which
being
diuided
into
90.
degrées
,
number
in
it
that
,
which
is
,
as
it
were
,
the
Eleuation
of
the
Pole
,
namely
17.
degrées
from
D.
towards
A.
Then
draw
the
line
of
Contingence
K.
L.
in
any
point
of
the
line
C.
D.
squire
wise
.
Take
with
your
compasses
the
least
distance
of
the
point
G.
and
of
the
Stile
:
extend
them
forth
in
the
line
C.
D.
I
meane
,
from
G.
toward
C.
make
there
a
point
marked
with
E.
vppon
which
point
or
centre
with
the
same
widenesse
of
the
compasses
,
drawe
the
Equator
from
H.
by
G.
to
I.
diuide
it
into
12.
equall
partes
,
&c.
Finish
that
which
remaineth
in
all
respects
,
like
to
the
Horizontall
Diall
,
in
naming
the
houres
,
drawing
of
the
lines
,
fixing
of
the
Stile
,
&c.
for
in
this
kinde
of
Diall
,
the
Stile
must
bée
fixed
in
the
centre
C.
standing
vpward
,
with
so
great
an
angle
,
as
C.
D.
F.
is
.
Beholde
the
Figure
folowing
.
A
South
Reclining
Erect
.
dialing diagram
The
making
of
a
North
Diall
Reclining
Direct
.
CAP.
12.
IN
these
kindes
,
if
the
Reclination
bée
lesse
then
the
Eleuation
of
the
Pole
,
subtract
that
from
this
,
&
kéep
the
remainder
for
the
Eleuation
of
the
Pole
:
according
to
which
Eleuation
,
make
a
North
Diall
Erect
Direct
,
and
it
will
be
fit
for
your
plat
.
In
which
the
houres
about
Noone
are
placed
,
being
profitable
onely
in
sommer
:
and
not
then
vnlesse
the
Reclination
be
greater
then
the
distance
of
the
Trop●k
of
S
,
from
the
Zenith
.
And
the
more
your
Diall
Reclineth
,
the
longer
time
it
will
shew
in
Sommer
.
Example
of
a
North
Diall
Reclining
45.
degrees
.
FIrst
I
take
the
Eleuation
of
the
Pole
(
which
wée
account
52.ᵈ.
)
〈◊〉
the
Reclination
of
the
plat
,
which
is
45.ᵈ.
and
there
remaineth
7.ᵈ.
which
shall
bée
in
place
of
the
Eleuation
of
the
Pole
.
Then
for
the
drawing
of
it
,
resort
to
the
North
Erect
Direct
,
because
their
Delineation
is
like
:
remembring
alwaies
to
call
that
which
remaineth
the
Eleuation
of
the
Pole
:
which
in
this
example
is
but
7.
degrées
.
In
the
figure
following
you
sée
that
most
part
of
the
houre
lines
bée
drawne
opposit
from
the
Contingent
,
beyond
the
centre
E.
as
you
must
doe
in
any
of
this
kinde
,
if
you
will
haue
the
houres
about
noone
.
dialing diagram
Example
of
a
North
Diall
Reclining
52.
degrees
.
BUt
if
the
Reclination
be
equal
with
the
Eleuation
of
the
Pole
:
then
describe
a
circle
vpon
the
centre
E.
and
diuide
it
into
24.
equall
partes
,
beginning
the
diuision
at
the
12.
houre
.
Draw
by
those
points
,
lines
for
the
houres
from
the
centre
E.
so
many
as
shall
be
necessarie
:
erecting
the
Stile
(
being
some
small
wier
)
in
the
centre
E.
right
vp
.
This
kinde
of
Diall
serueth
only
when
the
Sunne
is
in
the
north
signes
,
which
be
♈
,
♉
,
♊
,
♋
,
♌
,
♍
.
A
North
Reclining
Direct
.
dialing diagram
You
may
with
the
help
of
a
smale
brasse
quadrant
and
a
néedle
placed
conueniently
make
this
a
portable
and
fit
Diall
for
any
Eleuation
of
the
Pole
.
Againe
,
if
the
Reclination
shall
excéede
the
Eleuation
of
the
Pole
:
adde
the
complement
of
the
reclination
to
the
Eleuation
,
and
with
that
number
as
if
it
were
the
Eleuation
of
the
Pole
,
make
your
Diall
altogether
like
a
Horizontall
,
and
it
shall
be
fit
for
your
plat
.
In
which
notwithstanding
in
winter
,
very
fewe
houres
will
shew
,
and
those
about
noone
:
and
yet
not
these
,
vnlesse
the
Reclination
shall
bée
greater
,
then
the
●●…hest
bending
of
the
Trop●ke
of
♑
,
from
the
Zenith
.
Example
of
a
North
Diall
reclining
80.
d.
FIrst
adde
the
complement
of
●he
reclination
of
the
plat
,
which
is
10.ᵈ.
to
the
Eleuation
of
the
Pole
52.ᵈ.
and
with
the
totall
number
62.ᵈ.
●●●f
it
were
the
Eleuation
of
the
Pole
,
make
a
Horizontall
Diall
,
as
is
shewed
cap.
3.
Alwaies
remember
to
call
the
two
numbers
added
together
,
the
Eleuation
of
the
Pole
.
A
North
reclining
Direct
.
dialing diagram
The
making
of
an
East
and
West
Diall
reclining
.
CAP.
13.
FIrst
multiplie
the
Sine
of
the
Eleuation
of
the
Pole
,
by
the
Sine
of
the
Reclination
of
the
plat
,
and
diuide
the
product
by
the
whole
Sine
:
whereof
shall
come
a
quotient
,
whose
arke
is
the
distance
of
the
Stile
,
from
the
Substile
.
Compare
the
Complement
of
this
distance
with
the
Complement
of
the
Eleuation
of
the
Pole
,
and
which
you
shall
find
least
,
multiply
the
Sine
thereof
by
the
whole
Sine
,
parting
the
Product
by
the
Sine
of
the
greater
.
The
quotient
shall
yéelde
an
arke
,
whose
Complement
shall
be
the
distance
of
the
Substile
from
the
Meridian
.
Example
of
an
East
or
West
Diall
,
reclining
45.
degrees
.
FIrst
,
I
multiplie
the
Sine
of
the
Eleuation
of
the
Pole
52.
degrées
being
78801.
by
the
Sine
of
the
Reclination
of
the
plat
,
which
is
70710.
&
the
product
5572018710
I
diuide
by
100000
the
whole
Sine
,
and
the
quotient
is
55720.
the
arke
whereof
is
33.ᵈ.
52.ᵐ.
which
is
the
distance
of
the
Substile
from
the
Stile
.
Then
I
compare
the
Complement
of
this
distance
,
which
is
56.ᵈ.
8.ᵐ.
with
the
Complement
of
the
Eleuation
of
the
Pole
,
which
is
38.ᵈ.
and
finding
the
Complement
of
the
Eleuation
to
be
least
,
I
multiply
61566
the
Sine
thereof
,
by
the
whole
Sine
:
and
the
Product
arising
thereof
is
6156600000
:
which
I
diuide
by
the
Sine
of
the
greater
,
which
is
the
Complement
of
the
distance
,
whose
Sine
is
83033.
And
the
quotient
74141
yéeldeth
an
arke
47.ᵈ.
51.ᵐ.
whose
Complement
is
42.ᵈ.
9.ᵐ.
which
is
the
distance
of
the
Substile
from
the
Meridian
.
First
draw
a
line
Parallele
to
the
Horizon
A.
B.
drawe
The
delineation
of
the
figure
.
another
squier
wise
,
C.
D.
Then
make
the
quadrant
from
A.
to
D.
Number
therein
the
distance
of
the
Substile
from
the
Meridian
(
which
wée
found
to
bée
in
our
example
42.ᵈ.
9.ᵐ.
)
from
A.
toward
D.
At
the
end
of
this
number
from
the
centre
C.
draw
the
line
for
the
Substile
,
C.
E.
Account
from
this
line
the
distance
betwéene
the
Stile
and
the
Substile
,
which
is
33.ᵈ.
52.ᵐ.
draw
likewise
at
the
end
of
this
number
from
C.
the
line
C.
G.
for
the
Stile
.
Let
the
line
of
Contingence
bée
squire
wise
to
the
Substile
in
any
point
where
you
will
.
Then
take
with
your
compasses
the
least
distance
betwéen
the
point
E.
and
the
line
of
the
Stile
:
with
that
widnesse
the
one
foote
remaining
in
E.
extend
the
other
in
the
line
of
the
Substile
toward
C.
make
there
the
point
F.
vpon
which
draw
the
Equator
from
H.
by
E.
to
I.
Diuide
it
into
12.
equall
partes
;
beginning
your
diuision
where
the
ruler
being
placed
vpon
the
centre
F.
and
the
intersection
of
the
Meridian
with
the
Contingent
shall
touch
the
equator
.
Lay
the
ruler
from
F.
by
each
of
those
markes
,
and
where
it
shall
touch
the
line
of
Contingence
,
there
make
markes
:
by
which
from
the
centre
C.
drawe
the
houre
lines
so
many
as
shall
be
necessary
.
The
line
A.
B.
is
the
Meridian
,
and
sheweth
the
12.
houre
.
Finish
all
other
thinges
,
as
in
the
rest
before
you
were
taught
.
Note
that
if
it
be
an
East
diall
,
you
must
make
the
quadrant
from
A.
to
D.
If
a
West
,
from
B.
to
D.
Finish
the
residue
as
before
,
&c.
An
East
or
West
reclining
.
dialing diagram
The
making
of
a
South
reclining
declining
Diall
.
CAP.
14.
FIrst
,
in
this
kinde
,
as
in
other
which
follow
,
you
must
finde
out
and
place
the
Meridian
,
the
Substile
,
and
the
Stile
,
which
being
done
,
that
which
remaineth
is
finished
as
in
those
before
.
Therefore
the
Declination
and
the
Reclination
of
the
plat
being
known
by
your
instrument
,
multiplie
the
Sine
of
the
Declination
by
the
Sine
of
the
complement
of
the
Reclination
,
diuiding
the
product
by
the
whole
Sine
.
The
quotient
Sine
shall
yéeld
an
Arke
,
whose
complement
shall
be
named
the
Complement
to
be
repeated
.
Afterward
augment
the
Sine
of
the
Complement
of
the
Declination
,
by
the
whole
Sine
,
diuide
the
Product
by
the
Sine
of
the
Complement
to
be
repeated
:
where
of
shall
come
a
Sine
,
whose
arke
shal
be
the
distance
of
the
Meridian
from
the
Horizon
.
Againe
,
multiply
the
Sine
of
this
distance
,
by
the
Sine
of
the
Complement
of
the
Reclination
,
parte
the
Product
by
the
whole
Sine
,
the
arke
of
whose
quotient
shal
be
called
the
Eleuation
of
the
Meridian
.
Then
compare
this
Eleuation
of
the
Meridian
,
with
the
Eleuation
of
the
Pole
,
and
which
you
shall
finde
least
,
subtract
that
from
the
greater
,
and
that
which
remaineth
kéep
,
(
for
it
shall
be
called
the
difference
kept
)
being
mindefull
which
of
them
was
the
greatest
.
This
done
,
multiply
the
Sine
of
the
Complement
to
be
repeated
,
by
the
Sine
of
the
difference
kept
:
diuiding
the
Product
by
the
whole
Sine
,
whereof
shall
come
a
Sine
,
whose
arke
shal
be
the
distance
of
the
Stile
from
the
substile
.
To
conclude
,
compare
the
Complement
of
this
distance
,
with
the
complement
of
the
difference
kept
,
and
which
you
shall
finde
least
,
multiply
the
Sine
thereof
by
the
whole
Sine
:
part
the
Product
by
the
Sine
of
the
greater
,
and
thereof
shall
come
a
Sine
,
the
Complement
of
whose
arke
shal
be
the
distance
of
the
Substile
from
the
Meridian
.
Example
of
a
South
Dial
-
Declining
18.
d.
-
Reclining
25.
d.
First
looke
out
in
the
Table
the
Sine
of
the
Declination
,
which
is
30901.
Then
the
Complement
of
the
Reclination
being
65.ᵈ.
the
Sine
hereof
is
90630.
Afterward
multiply
90630
:
by
30901.
and
the
product
2800557630
diuide
by
the
whole
Sine
,
which
is
100900.
the
quotient
shal
be
28005.
whose
arke
is
16.ᵈ.
16ᵐ.
The
complement
whereof
being
73.ᵈ.
44.ᵐ.
is
the
complement
to
be
repeated
.
This
done
,
multiply
95105
the
Sine
of
the
Complement
of
the
Declination
72.ᵈ.
by
the
whole
Sine
100000.
the
product
shal
be
9510500000.
which
being
diuided
by
95996
the
Sine
of
the
complement
to
be
repeated
,
the
quotient
shal
be
99071
,
whose
arke
is
82.ᵈ.
11.ᵐ.
which
is
the
distance
of
the
Meridian
from
the
Horizon
.
Afterward
augment
the
Sine
of
this
distance
99071.
by
the
Sine
of
the
complement
of
the
Reclination
,
which
is
90630.
and
the
product
8978804730
part
by
the
whole
Sine
:
and
the
quotient
89788
shall
yéeld
an
arke
63.ᵈ.
53.ᵐ.
which
is
the
Eleuation
of
the
Meridian
.
Then
compare
the
Eleuation
of
the
Meridian
,
with
the
Eleuation
of
the
Pole
,
which
in
this
example
is
52.ᵈ.
and
finding
the
Eleuation
of
the
Pole
to
be
least
,
substract
this
namely
52.
degrées
)
from
63.ᵈ.
53.ᵐ.
the
Eleuation
of
the
Meridian
,
and
there
remaineth
11.ᵈ.
53.ᵐ.
which
is
the
difference
kept
.
Now
multiply
95996
being
the
Sine
of
the
Complement
to
be
repeated
,
which
is
20591.
the
product
is
1976653636.
which
diuided
by
the
whole
Sine
,
the
quotient
shal
be
19766
,
whose
arke
11.ᵈ.
24.ᵐ.
is
the
distance
of
the
Stile
from
the
Substile
.
Then
to
conclude
.
the
Complement
of
this
distance
,
which
is
78.ᵈ.
36.ᵐ.
being
compared
with
the
Complement
of
the
difference
kept
,
which
is
78.ᵈ.
7.ᵐ.
you
shall
finde
the
Complement
of
this
difference
kept
to
be
least
,
wherefore
multiply
97856
the
Sine
thereof
,
by
the
whole
Sine
,
and
the
product
9785600000.
part
by
the
Sine
of
the
greater
,
to
wit
,
of
the
Complement
of
the
distance
of
the
Stile
from
the
Substile
,
which
is
98027.
the
quotient
shal
be
99825.
whose
arke
is
86.ᵈ.
37.ᵐ.
The
Complement
whereof
is
3.ᵈ.
23.ᵐ.
which
is
the
distance
of
the
Substile
from
the
Meridian
.
There
be
thrée
sundry
kindes
of
these
Dials
,
the
one
differing
from
the
other
.
The
first
kinde
.
Marke
therefore
,
if
the
Eleuation
of
the
Meridian
be
greater
then
the
Eleuation
of
the
Pole
,
drawe
a
line
parallele
to
the
Horizon
A.
B.
out
of
the
middest
whereof
extend
an
other
C.
D.
squire
wise
to
the
line
A.
B.
make
the
quadrant
from
A.
to
D.
number
therin
from
A.
towards
D.
the
distance
of
the
Meridian
from
the
Horizon
,
which
is
82.ᵈ.
11.ᵐ.
at
the
end
hereof
from
the
centre
C.
draw
the
line
C.
E.
for
the
Meridian
.
From
which
account
backward
towards
A.
the
distance
of
the
Substile
from
the
Meridian
,
which
is
3.ᵈ.
23.ᵐ.
draw
at
the
end
of
this
number
the
line
C.
F.
for
the
Substile
.
Then
from
the
Substile
toward
A.
number
the
distance
of
the
Substile
from
the
Stile
11.ᵈ.
24ᵐ.
and
at
the
end
therof
extend
the
line
C.
G.
which
shall
represent
the
Stile
.
This
done
,
in
the
line
of
the
Substile
in
the
point
F.
(
which
you
may
take
where
you
wil
in
the
Substile
)
draw
the
line
of
Contingence
squirewise
to
the
Substile
.
Then
take
the
least
distance
of
the
point
F.
from
the
Stile
.
Afterward
extend
your
compasses
,
the
one
foote
being
placed
in
F.
in
the
line
of
the
Substile
toward
C.
vnto
H.
Describe
vpon
the
centre
H.
the
Equinoctiall
circle
by
F.
Diuide
it
into
24.
equall
partes
,
beginning
where
the
ruler
shall
touch
the
Equator
,
being
placed
vpon
the
centre
H
and
vpon
euery
marke
of
the
Equator
,
and
where
the
ruler
shall
touch
the
line
of
Contingence
,
there
make
markes
,
by
which
,
from
the
centre
C.
draw
the
houre
lines
somany
as
shall
be
necessary
,
C
▪
E.
alwaies
she
wing
the
12.
hower
.
Let
the
Stile
hang
directly
ouer
the
Substile
with
so
great
an
angle
as
F
C.
G.
is
:
fixing
it
in
the
centre
C.
pointing
▪
downward
to
the
Pole
Antartick
.
Place
the
line
A.
B.
parallele
to
the
Horizon
,
hauing
afterward
as
other
preparatiue
lines
no
vse
.
A
South
Declining
Reclining
.
dialing diagram
The
second
kinde
.
But
if
the
Eleuation
of
the
Pole
,
and
the
Eleuation
of
the
Meridian
be
found
equall
,
the
making
of
your
Diall
differeth
from
the
former
:
yet
the
finding
out
of
the
Meridian
and
the
Substile
,
&c.
is
wrought
as
in
the
other
before
,
whither
you
may
resorte
.
It
shal
be
sufficient
here
to
shew
an
example
of
this
kinde
.
Example
of
a
South
Diall
,
whose
-
Declination
is
,
32
d.
-
Reclination
is
,
33.d.
30.ᵐ.
-
Eleuation
of
the
Pole
is
,
52.d.
2.ᵐ.
First
I
multiply
52991
the
Sine
of
the
declination
,
by
83388
the
Sine
of
the
Complement
of
the
Reclination
,
and
the
product
4418813508
arising
thereof
,
I
diuide
by
the
whole
Sine
:
the
quotient
Sine
44188
yéeldeth
an
ark
26.ᵈ.
14.ᵐ.
whose
complement
being
63.ᵈ.
46.ᵐ.
is
the
complement
to
be
repeated
.
Then
I
increase
the
Sine
of
the
Complement
of
the
declination
,
which
is
84804
,
by
the
whole
Sine
,
and
the
product
is
,
8480400000
:
which
I
parte
by
89700
being
the
Sine
of
the
complement
to
be
repeated
.
The
arke
of
whose
quotient
Sine
94541
being
70.ᵈ.
59.ᵐ.
is
the
distance
of
the
Meridian
from
the
Horizon
.
This
done
,
I
multiply
this
Sine
94541
,
by
the
Sine
of
the
complement
of
the
reclination
,
which
is
83388
,
and
the
product
arising
hereof
,
being
7883584908
I
diuide
by
the
whole
Sine
:
the
quotient
therof
is
78835
,
whose
ark
52.
2ᵐ.
is
the
Eleuation
of
the
Meridian
,
which
I
compare
with
the
Eleuation
of
the
Pole
,
and
finding
them
equall
,
I
end
my
worke
héere
.
For
this
shal
be
sufficient
in
this
kinde
of
Diall
,
as
you
may
more
plainely
perceiue
by
the
delineation
of
the
Figure
.
Wherefore
if
the
Eleuation
of
the
Pole
,
and
of
the
Meridian
be
found
equall
,
(
as
in
this
example
it
is
)
make
a
line
parallel
to
the
Horizon
A.
B.
Draw
another
C.
D.
making
right
angles
with
the
line
A.
B.
Draw
the
quadrant
from
A.
to
D.
number
therein
the
distance
of
the
Meridian
from
the
Horizon
from
A.
toward
D.
which
is
70.ᵈ.
59.ᵐ.
being
here
in
place
of
the
Substile
.
Then
draw
the
line
of
Contingence
squire
wise
to
the
Meridian
C.
E.
(
which
is
also
the
Substile
C
E.
in
any
point
thereof
,
as
before
.
Place
one
foot
of
your
Compasses
in
the
intersection
E.
then
set
the
other
foote
in
the
Meridian
(
or
Substile
)
being
of
any
widenes
:
make
there
the
point
or
centre
F.
vpon
which
centre
drawe
the
halfe
Equator
from
G.
by
E.
to
H.
Diuide
the
one
half
therof
from
E.
to
H.
into
90.ᵈ.
Account
therein
from
the
Meridian
E.
towards
H.
the
declination
of
the
plat
32.ᵈ.
place
the
ruler
vpon
the
centre
F.
and
the
end
of
this
number
,
and
where
it
shall
touch
the
Contingent
line
,
there
make
a
marke
,
by
this
marke
you
must
draw
a
line
squire
wise
to
the
Contingent
line
,
which
shall
be
for
the
12
hower
.
And
where
the
ruler
shall
touch
the
Equator
,
there
begin
to
diuide
it
into
12.
equall
partes
,
by
which
lay
the
ruler
from
the
centre
F.
making
in
the
line
of
Contingence
markes
for
the
other
hower
lines
,
all
which
shall
cut
the
Contingent
line
squire-wise
.
Note
that
sometime
in
diuiding
of
the
Equator
,
the
two
parts
at
both
ends
next
to
the
Semidiameter
G.
H
shall
both
of
them
make
but
one
whole
parte
vnlesse
you
will
make
a
whole
circle
for
the
Equator
,
and
diuide
it
into
24.
partes
.
Let
the
Stile
be
a
small
wyer
standing
right
vp
in
the
point
E.
being
so
long
as
the
semidiameter
of
the
Equator
.
It
may
be
also
a
plate
of
iron
or
brasse
fastened
in
the
Substile
so
broad
as
the
Semidiameter
is
,
as
in
the
East
and
West
erect
dialls
,
&c.
Let
the
line
A.
B.
be
parallele
to
the
Horizon
.
Finish
all
other
things
as
before
.
A
South
reclining
declining
.
dialing diagram
The
third
kinde
.
If
the
Eleuation
of
the
Meridian
be
lesse
then
the
Eleuation
of
the
Pole
,
the
making
of
this
Diall
i●
vnlike
to
both
the
other
mentioned
before
,
yet
the
finding
out
of
the
distance
of
the
Stile
from
the
Substile
is
done
like
to
the
first
kinde
,
as
by
the
example
following
may
appeare
.
Example
of
a
South
Diall
-
Declining
45.
d.
-
Reclining
45.
d.
-
Eleuation
of
the
Pole
52.
d.
First
I
multiply
the
Sine
of
the
declination
being
7071
▪
by
the
Sine
of
the
complement
of
the
reclination
which
is
likewise
70710
,
and
the
product
4999904100
I
part
by
the
whole
Sine
.
The
quotient
is
49999
whose
arke
is
30.ᵈ.
The
Complement
of
this
arke
is
60.ᵈ.
which
is
the
Complement
to
be
repeated
.
Then
I
increase
the
Sine
of
the
Complement
of
the
declination
,
which
is
likewise
70710
,
by
the
whole
Sine
,
and
the
product
thereof
7071000000
I
diuide
by
the
Sine
of
the
Complement
to
be
repeated
86602
:
the
quotient
Sine
81649
yéeldeth
an
arke
54.ᵈ.
44.ᵐ.
which
is
the
distance
of
the
Meridian
from
the
Horizon
.
Afterward
I
multiply
this
Sine
81649
,
by
the
Sine
of
the
Complement
of
the
Reclination
,
which
is
70710
:
the
product
arising
5773400790
I
part
by
the
whole
Sine
,
the
quotient
is
57734.
The
arke
whereof
is
35.ᵈ.
16.ᵐ.
the
Eleuation
of
the
Meridian
:
which
I
compare
with
the
Eleuation
of
the
Pole
(
being
in
our
example
)
52.ᵈ.
and
finding
the
Meridian
Eleuation
to
be
least
,
I
substract
it
out
of
the
Eleuation
of
the
Pole
,
&
there
remaineth
16.ᵈ.
44.ᵐ.
which
is
the
difference
kept
.
This
done
,
I
augment
86602
the
Sine
of
the
Complement
to
be
repeated
,
by
28791
the
Sine
of
the
difference
kept
,
and
the
product
2493358182
comming
hereof
,
I
diuide
by
the
whole
Sine
,
the
quotient
Sine
24933
yéeldeth
an
arke
14.ᵈ.
26.ᵐ.
the
distance
of
the
Stile
from
the
Substile
.
Now
comparing
the
Complement
of
this
distance
being
75.ᵈ.
34.ᵐ.
with
the
Complement
of
the
difference
kept
,
which
is
73.ᵈ.
16.ᵐ.
and
séeing
the
Complement
of
the
difference
kept
to
be
least
:
I
multiply
95765
the
Sine
thereof
,
by
the
whole
Sine
,
and
the
product
9576500000
I
diuide
by
96843
the
Sine
of
the
complement
of
the
distance
,
and
98886
shal
be
the
quotient
therof
,
whose
arke
is
81.ᵈ.
27.ᵐ.
The
Complement
of
this
arke
is
8.ᵈ.
33.ᵐ.
which
is
the
distance
of
the
Substile
from
the
Meridian
.
In
the
Delineation
of
this
diall
,
drawe
first
as
before
a
line
Parallele
to
the
Horizon
A
B.
extend
another
C.
D.
making
right
angles
with
the
line
A.
B.
Draw
the
Quadrant
from
A.
to
D.
diuide
it
into
90.
degrées
.
In
which
account
the
distance
of
the
Meridian
from
the
Horizon
,
from
A.
towards
D.
which
is
54.ᵈ.
44.ᵐ.
drawe
at
the
ende
of
this
number
the
Meridian
line
from
the
centre
C.
which
shall
shew
the
12.
hower
.
Account
from
this
toward
D.
the
distance
of
the
Substile
from
the
Meridian
,
which
is
8.ᵈ.
33.ᵐ.
at
the
end
hereof
extend
from
C.
the
line
E.
for
the
Substile
.
From
this
,
number
the
distance
of
the
Stile
being
14.ᵈ.
26.ᵐ.
toward
D.
if
there
be
so
much
space
,
if
not
,
account
it
from
the
Substile
toward
A.
make
at
the
end
of
this
number
the
line
C.
F.
for
the
Stile
.
Let
the
line
of
Contingence
cut
the
Substile
squire-wise
,
in
what
poynt
you
will
.
Finish
all
other
things
,
as
in
the
first
of
these
thrée
kindes
of
South
reclining
declining
Dials
.
In
this
kinde
of
reclining
Dials
,
whose
Stile
must
bée
placed
from
the
centre
C.
vpward
toward
the
Pole
Artick
:
if
at
any
time
you
cannot
draw
to
both
ends
of
the
Contingent
line
so
many
howre
lines
as
shall
be
necessarie
:
then
prolong
beyond
the
centre
C.
the
lines
opposite
on
the
other
side
.
As
if
you
would
make
the
8.
houre
line
for
the
morning
,
draw
the
8.
for
the
euening
beyond
the
centre
C.
and
you
shall
haue
your
desire
.
Note
that
moreouer
,
in
this
kinde
contrarie
to
the
other
before
,
if
the
plat
decline
toward
the
West
,
(
as
in
this
example
it
doth
)
then
draw
the
quadrant
towards
the
West
,
&c.
But
if
the
Declination
be
towards
the
East
,
make
the
quadrant
towards
the
East
.
A
South
reclining
,
declining
.
dialing diagram
The
making
of
a
North
reclining
declining
Diall
.
CAP.
15.
The
first
kinde
.
IN
this
kinde
as
in
the
South
before
:
first
multiply
the
Sine
of
the
Declination
,
by
the
Sine
of
the
Complement
of
the
Reclination
:
parting
the
product
by
the
whole
Sine
.
The
quotient
Sine
thereof
shall
yéelde
an
arke
,
whose
Complement
shall
be
called
the
Complement
repeated
.
Then
increase
the
Sine
of
the
Complement
of
the
Declination
by
the
whole
Sine
,
diuide
the
product
by
the
Sine
of
the
Complement
repeated
:
the
quotient
Sine
thereof
will
giue
an
arke
,
which
shall
be
the
distance
of
the
Meridian
from
the
Horizon
.
The
same
quotient
Sine
multiply
by
the
Sine
of
the
Complement
of
the
reclination
:
and
the
number
arising
part
by
the
whole
Sine
:
the
arke
of
this
quotient
is
the
Eleuation
of
the
Meridian
.
Now
adde
the
Eleuation
of
the
Pole
to
the
Eleuation
of
the
Meridian
,
and
the
totall
number
or
arke
hereof
,
wée
will
call
the
compounded
arke
.
And
if
the
compounded
arke
be
lesse
then
90.
degrées
:
then
multiply
the
Sine
therof
,
by
the
Sine
of
the
Complement
repeated
,
diuiding
the
product
by
the
whole
Sine
:
and
hereof
shall
arise
a
quotient
Sine
,
whose
arke
shal
be
the
distance
of
the
Stile
from
the
Substile
.
Now
compare
the
Complement
of
this
distance
,
with
the
Complement
of
the
compounded
arke
:
and
increase
the
Sine
of
the
lesser
by
the
whole
Sine
,
part
the
product
by
the
Sine
of
the
greater
:
and
thereof
shall
come
a
Sine
,
the
Complement
of
whose
arke
shal
be
the
distance
of
the
Substile
from
the
Meridian
.
But
marke
here
the
diuersitie
which
doth
arise
by
reason
of
the
compounded
arke
:
for
hereby
you
shall
haue
thrée
sundry
waies
,
both
in
finding
out
the
distances
betwéene
the
Meridian
and
the
Horizon
,
the
Stile
and
Substile
,
&c.
And
likewise
in
the
delineation
of
the
figure
.
Whereof
ariseth
thrée
sundry
kinds
of
Dialls
:
the
first
of
them
being
already
taught
.
The
second
kinde
.
If
the
compounded
arke
be
iust
90.
degrées
:
then
the
distance
of
the
Stile
from
the
Substile
shall
be
the
Complement
repeated
:
and
the
distance
of
the
Substile
from
the
Meridian
shall
be
also
90.
degrées
.
Note
that
in
the
working
hereof
,
there
is
no
difference
from
the
first
kinde
.
For
here
as
in
the
other
before
,
you
shall
first
●inde
out
the
complement
repeated
:
then
the
distance
of
the
Meridian
from
the
Horizon
:
Afterward
the
Eleuation
of
the
Meridian
,
which
being
added
to
the
Eleuation
of
the
Pole
,
if
the
totall
number
bée
iust
90.ᵈ.
you
shall
not
néede
to
procéede
forward
,
for
this
(
as
before
I
made
mention
)
shall
bée
the
distance
of
the
Meridian
from
the
Substile
.
In
this
kinde
you
shall
haue
no
intersection
of
the
Meridian
and
the
Contingent
line
:
therefore
you
shall
begin
the
diuision
of
the
Equator
at
the
line
of
the
Substile
,
which
shall
shew
the
6.
houre
,
either
in
the
morning
,
or
euening
,
according
as
the
plat
doth
decline
.
The
third
kinde
.
But
if
the
compounded
arke
be
greater
then
90
degrées
,
substract
it
from
180
,
and
that
which
remayneth
shal
be
called
the
difference
kept
.
Then
multiplie
the
Sine
of
the
Complement
repeated
,
by
the
Sine
of
the
difference
kept
,
diuiding
the
product
by
the
whole
Sine
,
hereof
shall
come
a
Sine
,
whose
arke
shall
be
the
distance
of
the
Stile
from
the
Substile
.
Then
compare
the
Complement
of
this
distance
,
with
the
Complement
of
the
difference
kept
,
increasing
the
Sine
of
the
lesser
by
the
whole
Sine
,
and
parting
the
product
by
the
Sine
of
the
greater
:
whereof
shall
come
a
Sine
,
the
Complement
of
whose
arke
,
being
taken
from
180
degrées
,
the
remaynder
shal
shew
how
much
the
line
of
the
Substile
must
be
distant
(
vpward
by
the
Horizon
)
from
the
Meridian
.
For
the
better
vnderstanding
of
these
thrée
kinds
,
mark
these
thrée
examples
following
,
with
the
delineation
of
their
figures
.
Example
of
a
North
Diall
,
whose
-
Declination
is
,
45.
d.
-
Reclination
45.
d.
-
Eleuation
of
the
Pole
52.
d.
First
I
worke
this
altogether
like
to
the
South
reclining
45.ᵈ.
declining
45.ᵈ.
vntill
I
haue
found
out
the
Eleuation
of
the
Meridian
.
Then
I
adde
the
Eleuation
of
the
Meridian
which
is
,
35.ᵈ.
16.ᵐ.
to
the
Eleuation
of
the
Pole
52.ᵈ.
the
totall
number
is
87.ᵈ.
16.ᵐ.
which
is
the
compounded
arke
:
and
being
lesse
then
90.ᵈ.
I
procéede
with
this
arke
,
&c.
Now
therefore
I
multiplie
the
Sine
of
this
compounded
arke
,
which
is
99884
,
by
the
Sine
of
the
complement
to
be
repeated
being
86602
,
and
the
product
8650154168
I
part
by
the
whole
Sine
.
The
quotient
thereof
is
86501
,
whose
arke
59.ᵈ.
54.ᵐ.
is
the
distance
betwéene
the
Stile
and
the
Substile
.
Then
I
compare
30.ᵈ.
6.ᵐ.
being
the
Complement
of
this
distance
,
with
▪
the
Complement
of
the
compounded
arke
,
which
is
2.ᵈ.
44.ᵐ.
and
finding
this
least
,
I
increase
4768
the
Sine
thereof
,
by
the
whole
Sine
,
diuiding
the
product
,
which
is
476800000
,
by
50151
the
Sine
of
the
greater
:
the
quotient
Sine
yéeldeth
an
arke
5.ᵈ.
27.ᵐ.
the
Complement
hereof
84.ᵈ.
33.ᵐ.
is
the
distance
of
the
Substile
from
the
Meridian
.
In
drawing
of
this
Diall
,
first
as
before
,
make
a
line
Parallele
to
the
Horizon
A
B.
Then
extend
the
line
C.
D.
cutting
the
other
squire-wise
.
Marke
the
intersection
or
centre
with
E.
draw
thereupon
a
circle
A.
B.
C.
D.
whose
two
quadrants
at
the
least
,
toward
A.
(
if
the
plat
decline
Westward
,
or
else
toward
B.
if
it
decline
Eastward
)
being
diuided
into
90.ᵈ.
each
of
them
,
number
therein
from
A.
towards
D.
the
distance
of
the
Meridian
from
the
Horizon
,
which
is
54.ᵈ.
44.ᵐ.
and
at
the
end
hereof
from
the
centre
●
.
draw
the
line
F.
for
the
Meridian
,
or
12.
houre
.
Account
from
this
vpward
toward
C.
the
distance
of
the
Substile
from
the
Meridian
,
bring
84.ᵈ.
33.ᵐ.
make
likewise
at
the
end
of
this
number
from
E.
the
line
for
the
Substile
.
Againe
number
from
hence
vpward
(
if
there
be
so
much
space
,
or
else
downward
)
59.ᵈ.
54.ᵐ.
which
is
the
distance
betwéen
the
Stile
and
the
Substile
,
and
at
the
ende
hereof
drawe
the
line
H.
for
the
Stile
.
Let
the
Contingent
line
cut
the
Substile
squire-wise
in
the
point
G.
which
you
may
take
in
any
place
of
the
Substile
.
Then
with
your
compasses
the
least
distance
of
this
point
G.
and
the
Stile
being
taken
,
with
that
widenesse
extend
them
forth
in
the
line
of
the
Substile
toward
E.
making
there
the
point
I.
vpon
which
draw
the
Equator
or
Equinoctiall
circle
.
This
done
place
the
ruler
vpon
the
centre
I.
and
the
intersection
of
the
Meridian
and
the
Contingent
line
,
and
where
it
shall
touch
the
Equator
there
begin
to
diuide
it
into
24.
equall
partes
.
Finish
all
other
things
,
as
in
those
which
went
before
.
A
North
reclining
declining
.
dialing diagram
The
second
kinde
of
North
Diall
,
reclining
45.
degrees
14.
minuts
,
declining
38.
degrees
.
IT
shall
not
bée
necessarie
to
shewe
an
example
of
this
second
kinde
,
because
the
Complement
repeated
,
the
distance
of
the
Meridian
from
the
Substile
,
and
betwéene
the
Stile
and
Substile
,
&c.
is
found
out
altogether
like
to
the
other
before
,
and
that
which
foloweth
.
Therefore
it
sufficeth
to
set
downe
the
number
of
these
distances
.
First
the
Complement
repeated
is
,
64.ᵈ.
18.ᵐ.
The
distance
of
the
Meridian
from
the
Horizon
is
,
60.ᵈ.
59.ᵐ.
The
Eleuation
of
the
Meridian
is
38.ᵈ.
which
I
adde
to
the
Eleuation
of
the
Pole
being
52.ᵈ.
and
the
totall
90.ᵈ.
is
the
compounded
arke
.
Draw
therefore
in
this
kinde
as
before
,
a
line
Parallel
to
the
Horizon
A
B.
make
another
squire-wise
,
C.
D.
Draw
the
two
quadrants
from
C.
by
A.
to
D.
diuiding
each
of
them
into
90.ᵈ.
Then
number
herein
the
distance
of
the
Meridian
from
the
Horizon
,
which
is
60.ᵈ.
59.ᵐ.
drawing
from
E.
at
the
end
here
of
,
the
line
F.
for
the
Meridian
.
From
this
account
90.ᵈ.
being
here
the
distance
of
the
Substile
from
the
Meridian
:
and
like
wise
at
the
end
of
this
number
from
E.
drawe
the
line
for
the
Substile
.
Againe
from
this
line
downward
,
(
because
there
is
no
space
vpward
,
)
account
the
Complement
repeated
64.ᵈ.
18.ᵐ.
which
here
we
take
for
the
distance
of
the
Stile
from
the
Substile
:
make
likewise
by
this
number
the
line
E.
H.
for
the
Stile
.
Let
the
Contingent
line
cut
the
Substile
squire-wise
in
any
place
.
Then
taking
the
least
distance
with
the
compasses
of
the
point
G
and
of
the
Stile
,
with
that
widensse
in
the
Substile
,
make
the
poynt
I.
vpon
which
draw
the
Equinoctiall
circle
by
G
And
because
here
,
(
as
in
all
other
Dials
,
where
the
compounded
arke
is
iust
90.ᵈ.
)
there
is
no
intersection
of
the
Meridian
,
and
the
Contingent
line
:
therefore
begin
the
diuision
of
the
Equator
into
24
equal
parts
at
the
Substile
,
which
in
this
kinde
shall
shew
the
sixt
houre
,
either
in
the
euening
or
morning
,
according
to
the
declination
of
the
plat
.
Place
the
ruler
vpon
the
centre
I.
and
so
many
of
these
parts
as
you
can
,
making
markes
in
the
line
of
Contingence
as
before
,
draw
the
houre
lines
by
them
,
&c.
finish
the
rest
as
in
the
other
.
A
North
Declining
Reclining
.
dialing diagram
Example
of
the
third
kinde
of
North
Diall
before
mentioned
.
-
Reclining
21.d.
30.ᵐ.
-
Declining
30.
d.
Héere
first
,
as
before
I
multiply
the
Sine
of
the
Declination
being
50000
,
by
93041
which
is
the
Sine
of
the
complement
of
the
Reclination
and
the
product
4652070000
I
part
by
the
whole
Sine
:
the
quotient
46520
yéeldeth
an
arke
27.ᵈ.
43.ᵐ.
The
complement
whereof
is
62.ᵈ.
17.ᵐ.
being
the
Complement
to
be
repeated
.
Then
I
encrease
86602
the
Sine
of
the
complement
of
the
Declination
by
the
whole
Sine
,
diuiding
the
product
,
by
88525
the
Sine
of
the
Complement
repeated
:
The
arke
of
the
quotient
Sine
97827
,
is
78.ᵈ.
2.ᵐ.
,
which
is
the
distance
of
the
Meridian
from
the
Horizon
.
This
done
,
I
augment
this
quotient
Sine
97827
,
by
the
Sine
of
the
Complement
of
the
reclination
,
which
is
93041
:
the
product
9101921907
I
distribute
by
the
whole
Sine
:
and
the
quotient
91019
giueth
an
arke
65.ᵈ.
32.ᵐ.
the
Eleuation
of
the
Meridian
.
Now
I
adde
65.ᵈ.
32.ᵐ.
being
the
Eleuation
of
the
Meridian
,
to
52.ᵈ.
the
Eleuation
af
the
Pole
,
and
the
totall
number
117.ᵈ.
32.ᵐ.
being
the
compounded
arke
,
because
it
is
greater
then
90.ᵈ.
I
substract
it
from
180
,
and
there
remaineth
62.ᵈ.
28.ᵐ.
which
is
the
Difference
kept
.
Afterward
I
multiply
88525
the
Sine
of
the
Complement
repeated
,
by
88674
the
Sine
of
the
difference
kept
,
parting
the
product
7849865850
by
the
whole
Sine
.
The
quotient
is
78498
whose
arke
is
51.ᵈ.
43.ᵐ.
which
is
the
distance
betwéen
the
Stile
and
the
Substile
.
Then
comparing
the
Complement
of
this
distance
,
being
38.ᵈ.
17.ᵐ.
with
the
complement
of
the
difference
kept
,
which
is
27.ᵈ.
32.ᵐ.
and
finding
this
to
be
least
,
I
amplifie
46226
the
Sine
thereof
,
by
the
whole
Sine
,
diuiding
the
product
4622500000
by
the
Sine
of
the
greater
,
which
is
61955
,
and
74612
the
quotient
comming
hereof
yéeldeth
an
arke
48.ᵈ.
15.ᵐ.
whose
Complement
being
41.ᵈ.
45.ᵐ.
I
take
out
of
180
,
and
the
remainder
is
138.ᵈ.
15.ᵐ.
the
distance
of
the
Substile
from
the
Meridian
.
The
delineation
of
the
Figure
.
First
as
before
,
draw
a
line
A.
B.
parallele
to
the
Horizon
.
Make
another
C.
D.
squire-wise
to
the
former
.
Draw
two
quadrants
at
the
least
C.
A.
D.
diuiding
ech
of
them
into
90.
degrées
,
number
therein
from
A.
toward
D.
the
distance
of
the
Meridian
from
the
Horizon
,
which
in
our
example
is
found
to
be
78.ᵈ.
2.ᵐ.
draw
at
the
end
hereof
from
E.
the
line
F.
for
the
Meridian
.
Then
account
from
this
vpward
138.ᵈ.
15.ᵐ.
being
the
distance
of
the
Substile
from
the
Meridian
,
drawing
likewise
at
the
end
of
this
number
from
E.
the
line
for
the
Substile
.
Afterward
account
from
this
line
(
on
which
side
you
will
)
51.
43ᵐ.
the
distance
betwéen
the
Stile
and
the
Substile
,
extending
the
line
E
H.
by
the
end
of
this
number
for
the
Stile
.
Let
the
Contingent
line
cut
the
Substile
squire-wise
in
any
point
where
you
will
.
Afterward
taking
with
your
compasses
the
least
distance
betwéene
the
point
G.
and
the
Stile
,
with
that
widenesse
in
the
Substile
toward
E.
make
the
point
I.
vpon
which
draw
the
Equinoctiall
circle
by
G.
And
because
in
this
kinde
,
where
the
Compounded
arke
is
greater
then
90.ᵈ.
there
is
none
intersection
of
the
Meridian
and
the
contingent
line
beneath
the
ceutre
E.
therefore
draw
forth
the
Meridian
beyond
the
centre
,
then
place
your
ruler
on
the
intersection
of
the.
Meridian
and
Contingent
line
aboue
the
centre
,
and
the
point
●
.
and
where
it
cutteth
the
Equator
,
there
begin
to
diuide
it
into
24.
equall
partes
.
Finish
that
which
remaineth
as
before
.
A
North
reclining
declining
.
dialing diagram
The
making
of
a
South
Inclining
direct
Diall
.
CAP.
16.
IF
the
inclination
of
the
plat
be
lesse
then
the
Eleuation
of
the
pole
,
take
that
from
this
,
accounting
the
remainder
for
the
Eleuation
of
the
Pole
.
And
with
this
number
as
if
it
were
the
Eleuafion
of
the
Pole
make
a
Diall
like
to
the
South
erect
direct
,
and
it
shall
be
fit
for
your
plat
.
But
if
the
Inclination
of
the
plat
be
equal
with
the
Eleuation
of
the
Pole
,
make
your
Diall
altogether
like
to
the
North
reclining
direct
,
whose
reclination
likewise
is
equall
to
the
Eleuation
of
the
Pole
.
They
differ
onely
herein
,
that
this
is
placed
downward
to
the
earth
,
and
that
vpward
.
But
if
the
Inclination
of
the
plat
be
greater
then
the
Eleuation
of
the
Pole
,
substract
this
from
that
,
and
with
the
number
remaining
,
as
if
it
were
the
Eleuation
of
the
Pole
,
make
your
Dial
like
to
the
North
erect
direct
.
Example
of
this
kinde
incling
65.
d.
Substract
52.ᵈ.
the
Eleuation
of
the
Pole
,
out
of
65.ᵈ.
being
the
Inclination
of
the
plat
,
and
the
remainder
13.ᵈ.
account
the
Eleuation
of
the
Pole
.
For
the
delineation
hereof
,
resort
to
the
North
erect
Diall
,
Cap.
5.
A
South
inclining
direct
.
dialing diagram
You
sée
in
this
Figure
,
that
all
the
lines
for
the
howers
are
drawen
opposite
from
the
Contingent
line
,
beyond
the
centre
E.
In
like
maner
must
you
doe
in
the
delineation
of
all
such
,
which
incline
more
then
the
eleuation
of
the
Pole
.
Let
the
Stile
in
this
kinde
be
placed
directly
ouer
the
Meridian
,
with
so
great
an
angle
as
D.
E.
F.
is
,
&c.
The
making
of
a
North
inclining
direct
Diall
.
CAP.
17.
IF
the
Inclination
of
the
plat
be
lesse
then
the
complement
of
the
Eleuation
of
the
pole
,
adde
the
inclination
to
the
Eleuation
:
and
with
that
number
,
as
if
it
were
the
Eleuation
of
the
Pole
,
make
a
North
erect
direct
diall
,
for
your
plat
.
But
if
the
inclination
be
equall
with
the
complement
of
the
Eleuation
of
the
Pole
,
then
make
a
Diall
as
you
were
taught
in
the
second
kinde
of
South
reclining
direct
:
for
as
that
plat
so
reclining
in
the
South
is
placed
vpward
:
so
is
this
placed
down
ward
.
Note
that
this
North
diall
sheweth
but
onely
4.
howers
,
the
two
first
in
the
morning
,
and
the
two
last
in
the
euening
,
and
that
only
in
the
middest
of
Sommer
.
But
if
the
inclination
be
greater
then
the
Complement
of
the
Eleuation
of
the
Pole
,
substract
this
lesser
out
of
the
other
being
greater
:
and
with
the
number
remaining
,
as
if
it
were
the
Eleuation
of
the
Pole
,
make
your
diall
like
to
an
Horizontall
.
This
kinde
likewise
sheweth
very
few
howers
.
Example
of
this
last
kinde
,
inclining
45.
d.
First
I
take
38.ᵈ.
being
the
complement
of
the
Eleuation
of
the
Pale
,
out
of
45.ᵈ.
the
inclination
of
the
plat
,
and
there
remaineth
7.ᵈ.
which
I
kéep
for
the
Eleuation
of
the
Pole
.
For
the
delineation
of
this
diall
,
resort
to
the
Horizontall
,
Cap.
3.
A
North
inclining
Direct
.
dialing diagram
The
making
of
the
East
and
West
inclining
Dials
.
CAP.
18.
MUltiply
the
Sine
of
the
Eleuation
of
the
Pole
by
the
Sine
of
the
Inclination
of
the
plat
,
diuiding
the
product
by
the
whole
Sine
:
the
quotient
arke
shall
be
the
distance
of
the
Stile
from
the
Substile
.
Then
compare
the
complement
of
this
distance
with
the
complement
of
the
Eleuation
of
the
Pole
,
increasing
the
Sine
of
the
lesser
by
the
whole
Sine
,
part
the
product
by
the
Sine
of
the
greater
,
where
of
shall
come
a
Sine
,
the
Complement
of
whose
arke
shal
be
the
distance
of
the
Substile
from
the
Meridian
.
It
shall
not
be
necessarie
to
shew
any
example
hereof
,
because
the
East
and
West
reclining
bée
altogether
like
to
this
.
Wherefore
resort
thither
,
for
the
working
of
your
example
,
for
those
distances
in
drawing
this
figure
shall
bée
here
obserued
.
The
delineation
of
an
East
Diall
,
inclining
45.
d.
First
drawe
a
line
Parallele
to
the
Horizon
,
A.
B.
make
the
perpendiculare
line
C.
D.
squire-wise
to
the
other
.
Describe
the
quadrant
from
A.
to
D.
number
from
A.
toward
D.
33.ᵈ.
52.ᵐ.
the
distance
of
the
Substile
from
the
Meridian
,
and
at
the
end
hereof
from
C.
draw
the
line
E.
for
the
Substile
,
account
from
this
42.ᵈ.
9.ᵐ.
drawing
likewise
at
the
end
of
this
number
the
line
G.
for
the
Stile
.
Let
the
Contingent
line
cut
the
Substile
squire-wise
.
Finish
all
things
els
,
as
in
the
East
reclining
.
An
East
and
West
inclining
.
dialing diagram
The
making
of
a
South
inclining
declining
Diall
.
CAP.
19.
FIrst
multiplie
the
Sine
of
the
Declination
,
by
the
Sine
of
the
complement
of
the
inclination
,
parting
the
product
by
the
whole
Sine
.
The
quotient
Sine
shall
yéeld
an
arke
,
whose
complement
shall
bée
named
the
complement
repeated
.
Then
increase
the
Sine
of
the
Complement
of
the
Declination
by
the
whole
Sine
,
and
the
product
diuide
by
the
Sine
of
the
Complement
repeated
:
whereof
shall
come
a
Sine
,
whose
arke
is
the
distance
of
the
Meridian
from
the
Horizon
.
Afterward
,
this
Sine
being
multiplied
by
the
Sine
of
the
Complement
of
the
inclination
,
and
the
product
parted
by
the
whole
Sine
:
the
arke
of
the
quotient
Sine
shall
bée
the
Eleuation
of
the
Meridian
.
Which
arke
you
must
adde
to
the
Eleuation
of
the
Pole
.
And
if
the
totall
number
bée
lesse
then
90.ᵈ.
it
shall
bée
named
the
Doubtfull
arke
.
But
if
it
be
greater
then
90.ᵈ.
take
it
from
180
,
and
let
the
remainder
be
called
the
Doutfull
arke
.
This
done
,
augment
the
Sine
of
the
Complement
repeated
,
by
the
Sine
of
the
Doutfull
arke
:
&
the
product
arising
thereof
being
diuided
by
the
whole
Sine
,
the
quotient
arke
shall
be
the
distance
of
the
Stile
from
the
Substile
.
Now
compare
the
Complement
of
this
distance
,
with
the
Complement
of
the
Doutful
arke
,
multiplying
the
Sine
of
the
lesser
,
by
the
whole
Sine
,
diuiding
the
product
by
the
Sine
of
the
greater
:
the
arke
of
the
quotient
Sine
comming
thereof
shall
bée
the
distance
of
the
Substile
from
the
Meridian
.
But
note
,
if
the
doubtfull
arke
be
found
without
subtraction
from
180
,
(
which
is
if
it
bée
lesse
then
90ᵈ.
)
then
you
must
subtract
the
distance
of
the
Substile
from
the
Meridian
out
of
180
,
and
the
number
remaining
shall
be
the
true
distance
of
the
Meridian
from
the
Substile
.
Marke
this
likewise
,
if
the
doubtfull
arke
be
equall
90
degrées
,
let
the
Complement
repeated
be
the
distance
of
the
Stile
from
the
Substile
:
then
shall
there
bée
iust
90ᵈ.
for
the
space
betwéene
the
Substile
and
the
Meridian
,
as
before
is
taught
in
the
North
declining
reclining
,
whither
you
may
resort
for
the
working
hereof
.
Here
it
shall
bée
sufficient
to
shew
two
examples
,
with
the
delineation
of
their
figures
:
the
one
,
where
the
doubtfull
arke
is
subtracted
from
180ᵈ.
and
the
other
,
where
there
is
no
subtraction
hereof
,
because
it
is
lesse
then
90
degrées
.
Example
of
a
South
Diall
-
Inclining
45
degrees
.
-
Declining
45
degrees
.
Forasmuch
as
this
is
altogether
like
to
the
North
reclining
45ᵈ.
declining
45ᵈ.
whither
you
may
resort
:
I
wil
omit
the
working
of
the
former
part
of
this
example
,
vntil
I
come
to
the
finding
out
of
the
distance
of
the
Substile
from
the
Meridian
.
The
former
part
of
this
example
you
may
finde
to
bée
thus
wrought
in
the
North
reclining
declining
:
-
1
First
the
complement
repeated
60ᵈ.
-
2
Then
the
distance
of
the
Meridian
from
the
Horizon
54ᵈ.
44ᵐ.
-
3
Next
the
Eleuation
of
the
Meridian
35ᵈ.
16ᵐ.
-
4
The
compounded
arke
there
,
which
we
call
the
doubtfull
arke
here
87ᵈ.
16
-
5ᵐ.
The
distance
of
the
Stile
from
the
Substile
59ᵈ.
54ᵐ.
-
6
Last
,
the
distance
of
the
Substile
from
the
Meridian
84ᵈ.
33ᵐ.
But
here
(
as
before
is
taught
)
you
must
subtract
this
distance
from
180ᵈ.
because
the
doubtfull
arke
was
lesse
then
90ᵈ.
and
then
the
remainder
95ᵈ.
27ᵐ.
shall
bée
the
true
distance
of
the
Substile
from
the
Meridian
.
In
the
delineation
of
this
diall
,
first
,
as
before
,
make
a
line
paralele
to
the
Horizon
A.
B.
Draw
another
perpendicular
C.
D.
cutting
the
former
squire-wise
.
Make
two
quadrants
from
A.
by
D
▪
to
B.
If
the
plat
decline
westward
,
number
the
distance
of
the
Meridian
from
the
Horizon
from
A.
toward
D.
&c.
But
if
the
declination
be
Eastward
(
as
in
this
example
it
is
)
then
account
this
distance
of
the
Meridian
from
the
Horizon
,
which
is
54ᵈ.
44ᵐ.
from
B.
toward
D.
drawing
at
the
ende
hereof
from
the
centre
C.
the
Meridian
line
which
shall
shew
the
12
houre
.
Account
likewise
from
that
toward
A.
95ᵈ.
27ᵐ.
the
distance
of
the
Substile
from
the
Meridian
:
making
in
like
maner
the
line
E.
C.
for
the
Substile
.
From
this
line
on
which
side
you
will
,
number
the
distance
of
the
Stile
from
the
Substile
,
being
59ᵈ.
54ᵐ.
drawe
by
this
the
line
G.
representing
the
Stile
.
Let
the
line
of
Contingence
cut
the
Substile
squire-wise
in
any
point
where
you
will
.
Make
the
Equator
,
begin
the
diuision
thereof
,
and
draw
the
houre
lines
in
all
respects
as
in
the
North
reclining
21
degrées
30
minutes
,
declining
30
degrées
.
Cap.
15.
A
South
declining
inclining
Diall
.
dialing diagram
The
second
example
of
a
South
Diall
-
Inclining
33.d.
40.m.
Where
the
doutfull
arke
is
subtracted
from
180.
-
Declining
31.d.
Where
the
doutfull
arke
is
subtracted
from
180.
First
51503
the
Sine
of
the
Declination
being
multiplied
,
by
83227
the
Sine
of
the
Complement
of
the
inclination
:
and
the
product
4286440181
diuided
by
the
whole
Sine
:
the
arke
of
the
quotient
is
25ᵈ.
23.ᵐ.
The
complement
whereof
being
64ᵈ.
37ᵐ.
is
the
complement
repeated
.
Then
I
increase
the
Sine
of
the
Complement
of
the
declination
which
is
85716
,
by
the
whole
Sine
,
and
I
part
the
product
8571600000
,
by
90346
the
Sine
of
the
Complement
repeated
.
The
quotient
94875
yeeldeth
an
arke
71ᵈ.
35ᵐ.
which
is
the
distance
of
the
Meridian
from
the
Horizon
.
Agayne
,
I
multiply
this
Sine
94875
,
by
the
Sine
of
the
Complement
of
the
Inclination
being
83227
,
and
the
product
7895961425
arising
thereof
,
I
diuide
by
the
whole
Sine
.
The
arke
of
the
quotient
is
52ᵈ.
9ᵐ
which
is
the
Eleuation
of
the
Meridian
.
Now
this
being
added
to
the
Eleuation
of
the
Pole
52ᵈ.
and
the
total
number
104ᵈ.
9ᵐ.
taken
from
180
,
there
remayneth
75ᵈ.
51ᵐ.
which
is
the
doubtful
arke
.
Therefore
I
augment
90346
the
Sine
of
the
Complement
repeated
,
by
96930
the
Sine
of
the
doubtful
arke
,
and
the
product
8760399890
I
parte
by
the
whole
Sine
.
The
arke
of
the
quotient
61ᵈ.
10ᵐ.
is
the
distance
of
the
Substile
from
the
Stile
.
This
done
,
I
compare
28.ᵈ.
50.ᵐ.
the
Complement
of
this
distance
,
with
14.ᵈ.
9.ᵐ.
the
Complement
of
the
doutfull
arke
,
multiplying
the
Sine
of
the
lesser
,
which
is
24446
,
by
the
whole
Sine
,
diuiding
the
product
2444600000
,
by
48226
the
Sine
of
the
greater
.
The
quotient
Sine
50741
yéeldeth
an
arke
30ᵈ.
30.ᵐ.
whose
Complement
59ᵈ.
30ᵐ.
is
the
distance
of
the
Substile
from
the
Meridian
.
First
draw
a
line
A.
B.
Parallele
to
the
Horizon
:
drawe
another
C.
D.
squire-wise
to
the
line
A.
B.
make
the
two
quadrants
The
delineation
of
the
figure
.
71.
from
A.
by
D.
to
B.
And
because
this
Declination
is
on
the
left
hand
,
number
from
A.
towards
D.
7ᵈ.
35ᵐ.
the
distance
of
the
Meridian
from
the
Horizon
,
drawing
by
this
from
C.
the
Meridian
line
.
From
that
toward
B.
account
59ᵈ.
30ᵐ.
the
distance
of
the
Substile
from
the
Meridian
,
making
in
like
manner
at
the
ende
of
this
number
from
C.
the
Substile
line
E.
Againe
from
this
forward
(
if
you
can
,
or
else
backward
)
number
the
distance
of
the
Stile
from
the
Substile
,
which
is
61ᵈ.
10ᵐ.
Draw
likewise
by
this
from
C.
the
line
G.
for
the
Stile
.
Let
the
Contingent
cut
the
Substile
squire-wise
in
any
place
,
where
you
will
,
&c.
The
making
of
the
reclining
declining
Dials
before
,
shall
teach
you
the
finishing
of
this
likewise
.
A
South
declining
inclining
.
dialing diagram
The
making
of
a
North
inclining
declining
Diall
.
CAP.
20.
THe
working
of
this
kinde
is
altogether
like
the
South
reclining
declining
diall
.
First
therefore
multiplie
the
Sine
of
the
Declination
,
by
the
Sine
of
the
Complement
of
the
inclination
,
diuiding
the
product
by
the
whole
Sine
.
The
quotient
shalt
giue
an
arke
:
whose
Complement
shall
be
named
the
Complement
repeated
.
Then
augment
the
Sine
of
the
Complement
of
the
Declination
by
the
whole
Sine
,
&
the
product
part
by
the
Sine
of
the
Complement
repeated
.
Whereof
will
come
a
quotient
Sine
:
whose
arke
shall
be
the
distance
of
that
which
is
as
it
were
the
Meridian
from
the
Horizon
.
For
the
finding
out
of
the
Eleuation
of
the
Meridian
,
because
it
may
bée
done
two
sundry
waies
,
I
will
set
them
downe
both
,
referring
the
choyse
to
your selfe
.
Compare
the
Complement
of
the
arke
last
found
out
,
with
the
Declination
of
the
plat
,
multiplying
the
Sine
of
the
lesser
,
by
the
whole
Sine
:
and
diuiding
the
product
by
the
Sine
of
the
greater
.
The
quotient
Sine
shall
yéeld
an
arke
:
whose
Complement
shall
be
the
Eleuation
of
the
Meridian
.
|
Or
multiply
the
Sine
of
the
arke
last
found
out
,
by
the
Sine
of
the
Complement
of
the
inclination
,
part
the
product
by
the
whole
Sine
:
and
the
arke
of
the
quotient
Sine
shal
be
the
Eleuation
of
the
Meridian
.
|
Now
comparing
the
Eluation
of
the
Pole
with
the
Eleuation
of
the
Meridian
,
subtract
the
lesser
from
the
greater
,
retaining
the
number
remaining
,
which
shall
be
called
the
difference
kept
.
Afterward
increase
the
Sine
of
the
difference
kept
,
by
the
Sine
of
the
Complement
repeated
,
and
diuide
the
product
by
the
whole
Sine
.
The
quotient
arising
of
this
diuision
shall
giue
an
arke
,
which
shall
be
the
distance
betwéene
the
Stile
and
the
Substile
.
To
conclude
,
the
Complement
of
this
distance
being
compared
with
the
Complement
of
the
difference
kept
,
multiplie
the
Sine
of
the
lesser
by
the
whole
Sine
,
and
part
the
product
by
the
Sine
of
the
greater
.
The
Complement
of
the
arke
of
the
quotient
Sine
,
shall
be
the
distance
of
the
Substile
from
the
Meridian
.
But
note
,
if
the
Eleuation
of
the
Meridian
,
&
the
Eleuation
of
the
Pole
be
found
equal
,
make
an
Equinoctial
dial
as
before
you
were
taught
in
the
Meridionall
reclining
declining
:
for
there
is
no
difference
,
but
only
that
this
is
placed
downward
,
and
the
South
vpward
.
There
be
of
this
north
,
as
of
the
South
reclining
declining
,
thrée
sundrie
kinds
of
Dials
,
as
by
the
examples
and
figures
following
you
may
perceiue
.
Example
of
a
North
Diall
First
example
.
-
Inclining
20
d.
-
Declining
30
d.
First
I
multiplie
50000
the
Sine
of
the
declination
,
by
93969
the
Sine
of
the
Complement
of
the
inclination
,
and
the
product
thereof
4698450000
,
I
diuide
by
the
whole
Sine
100000
,
&
the
quotient
Sine
46984
yéeldeth
an
arke
28ᵈ.
2ᵐ.
whose
Complement
61ᵈ.
58ᵐ.
is
the
Complement
repeated
.
Then
I
augment
the
Sine
of
the
Complement
of
the
declination
,
which
is
86602
by
the
whole
Sine
,
parting
the
product
8660200000
,
by
88267
the
Sine
of
the
Complement
repeated
:
the
quotient
is
98113.
The
arke
therof
being
78ᵈ.
51ᵐ.
is
the
distance
of
the
Meridian
from
the
horizon
.
Now
in
comparing
the
Complement
Two
waies
in
working
the
example
,
for
the
two
precepts
,
of
the
finding
out
the
Eleuation
of
the
Meridian
.
of
the
arke
last
found
out
,
with
the
declination
of
the
plat
:
I
find
the
Complement
of
the
arke
least
.
Wherfore
I
multiply
the
Sine
therof
being
19337
by
the
whole
Sine
:
and
the
product
1933700000
,
I
diuide
by
50000
the
Sine
of
the
greater
.
The
quotient
38673
giueth
an
Both
these
waies
tend
to
one
end
.
arke
22ᵈ.
46ᵐ.
whose
Complement
67ᵈ.
14ᵐ.
is
the
Eleuation
of
the
Meridian
.
|
Or
multiplie
98112
the
Sine
of
the
arke
last
found
out
,
by
the
Sine
of
the
Complement
of
the
inclination
,
which
is
93969
:
and
the
product
9219566568
part
by
the
whole
Sine
.
The
quotient
shall
bée
92195
,
whose
arke
67
degrées
14
minutes
is
the
Eleuation
of
the
Meridian
.
|
This
done
,
I
compare
the
Eleuation
of
the
Meridian
67ᵈ.
14ᵐ.
with
the
Eleuation
of
the
Pole
52ᵈ.
subtracting
the
lesser
from
the
greater
,
and
there
remaineth
15ᵈ.
14ᵐ.
which
is
the
difference
kept
.
Then
I
multiply
26275
the
Sine
of
the
difference
kept
,
by
88267
the
Sine
of
the
Complement
repeated
:
parting
the
product
2318455682
,
by
the
whole
Sine
.
The
arke
11.ᵈ.
47.ᵐ.
of
the
quotient
Sine
23184
,
is
the
distance
of
the
Stile
from
the
Substile
.
Now
the
Complement
of
this
distance
being
76.ᵈ.
36ᵐ.
compared
with
74.ᵈ.
47.ᵐ.
the
Complement
of
the
difference
kept
,
I
encrease
96494
the
Sine
of
the
lesser
,
by
the
whole
sine
,
and
the
product
therof
9649400000
,
I
distribute
by
97277
the
Sine
of
the
greater
.
And
the
quotient
is
99191.
whose
arke
is
82.ᵈ.
43.ᵐ.
The
complement
wherof
being
7.ᵈ.
17.ᵐ.
is
the
distance
of
the
Substile
from
the
Meridian
.
The
delineation
of
the
Diall
.
If
the
Equator
of
the
Meridian
be
greater
then
the
Elenation
of
the
Pole
,
draw
a
line
A.
B.
parallele
to
the
Horizen
,
make
another
C.
D.
squire-wise
to
the
former
,
describe
the
quadrant
on
the
left
hand
from
A.
to
C.
(
because
the
Declination
is
on
the
right
hand
)
numbring
therin
from
A.
vpward
76.ᵈ.
32.ᵐ.
the
distance
of
the
Meridian
from
the
Horizon
,
draw
at
the
end
thereof
from
D.
the
line
G.
representing
the
Meridian
.
From
this
backward
,
toward
A
account
the
distance
of
the
Substile
from
the
Meridian
,
which
is
7.ᵈ.
41.ᵐ.
making
likewise
at
the
end
of
this
number
from
D.
the
line
E.
for
the
Substile
.
From
hence
account
11.ᵈ.
47.ᵐ.
being
the
distance
of
the
Stile
from
the
Substile
,
drawing
in
like
maner
from
D.
the
line
F.
for
the
Stile
.
Let
the
line
of
contingence
cut
the
Substile
squirewise
as
before
,
make
the
Equator
in
this
,
as
in
the
other
before
.
Place
the
ruler
vpon
the
centre
H.
and
the
intersection
of
the
Contingent
line
,
and
the
Meridian
,
beginning
the
diuision
thereof
into
24.
equall
parts
,
where
the
ruler
shall
touch
the
Equator
.
Finish
all
things
remaining
,
as
before
.
Remember
that
in
this
kinde
of
North
inclining
declining
Diall
,
the
Meridian
line
rather
representeth
the
12.
houre
at
midnight
,
then
in
the
day
:
wherefore
in
accounting
the
houre
lines
,
let
the
meridian
be
alwaies
for
the
12.
hower
in
the
night
.
And
then
if
your
plat
decline
Westward
,
account
backward
as
it
were
11.
10.
9.
which
howers
with
the
12.
you
may
omit
in
the
delineation
of
your
diall
,
because
they
haue
no
vse
in
our
Eleuation
.
But
account
forward
8
,
7
,
6
,
5
,
4.
&c.
so
many
as
you
think
shall
be
necessary
,
for
some
declination
will
receiue
more
,
then
other
will
:
the
greater
the
more
,
the
lesser
the
sewer
howers
.
But
if
the
declination
of
your
plat
be
Eastward
then
account
from
the
Meridian
line
forward
1
,
2
,
3
,
4.
&c.
so
many
as
shall
be
néedfull
,
omitting
likewise
the
first
thrée
,
&c.
A
North
inclining
declining
.
dialing diagram
The
second
kinde
.
But
if
the
Eleuation
of
the
Meridian
,
and
the
Eleuation
of
the
Pole
be
equall
,
the
making
of
the
Diall
differeth
from
the
other
before
.
For
an
example
hereof
,
and
the
drawing
of
the
Figure
,
resorte
to
the
South
reclining
33ᵈ.
30.ᵐ.
declining
32.ᵈ.
for
these
are
both
alike
,
only
remember
here
,
that
if
this
decline
Eastward
,
make
the
quadrant
likewise
on
the
East
side
,
&c.
But
if
the
plat
decline
toward
the
West
,
make
the
quadrant
Westward
(
as
in
the
figure
following
)
finishing
all
things
els
as
here
you
sée
done
.
Obserue
the
same
order
in
naming
the
howre
lines
which
I
taught
you
before
.
A
North
inclining
declining
.
dialing diagram
The
third
Example
of
a
North
Diall
.
-
Inclining
45.
d.
-
Declining
45.
d.
If
the
Eleuation
of
the
Meridian
be
lesser
then
the
Eleuation
of
the
Pole
,
make
your
Diall
thus
,
For
the
working
of
the
example
,
and
the
delineation
of
the
figure
,
resorte
to
the
South
reclining
45.ᵈ.
declining
45.ᵈ.
for
that
agréeeth
with
this
,
except
only
that
in
this
,
the
Stile
is
placed
downward
,
and
sheweth
but
fewe
howres
,
and
those
likewise
are
drawen
downward
:
but
in
the
other
the
Stile
standeth
vpward
,
shewing
many
houres
,
and
those
likewise
for
the
most
part
are
drawen
vpward
.
Marke
also
in
this
kinde
,
if
your
plat
decline
westward
,
draw
the
Quadraut
on
the
West
side
,
but
if
the
declination
be
Eastward
,
make
the
Quadrant
on
the
East
side
,
&c.
The
making
of
these
,
are
more
pleasant
to
know
,
then
profitable
to
vse
:
vnlesse
the
declination
be
the
greater
,
for
so
it
may
shew
the
more
howres
.
For
the
naming
of
the
howres
,
doe
as
you
were
taught
before
in
the
first
of
these
thrée
kindes
.
A
North
Declining
Inclining
.
dialing diagram
The
delineation
of
those
Dials
,
whose
plat
lyeth
nigh
to
the
Eleuation
of
the
Pole
.
CAP.
21.
WHen
as
the
declination
and
reclination
,
or
declination
and
inclination
,
shall
cause
the
plat
of
your
Diall
to
lye
nigh
to
the
Eleuation
of
the
Pole
,
then
the
hower
lines
must
be
drawen
very
long
,
to
make
the
distances
somwhat
large
,
so
that
they
may
be
discerned
one
from
another
.
And
commonly
these
folowing
be
such
as
here
we
meane
.
A
South
-
Reclining
direct
.
-
Declining
erect
.
-
Declining
reclining
.
An
Eastor
West
-
Reclining
.
-
Inclining
.
A
North
-
Inclining
direct
.
-
Declining
erect
.
-
Declining
inclining
.
In
all
these
kindes
oftentimes
the
distance
betwéen
the
Stile
and
the
Substile
is
so
small
that
it
is
not
possible
to
draw
your
Diall
,
except
the
plat
be
very
large
:
which
at
al
times
you
shall
not
haue
.
Therefore
the
best
way
is
this
.
First
drawe
your
Diall
very
true
(
as
before
hath
béen
taught
)
vpon
a
large
paper
,
making
your
quadrant
so
great
as
may
be
.
Draw
likewise
the
howre
lines
very
long
,
which
will
cause
the
greater
distance
betwéen
the
Stile
and
the
Substile
,
and
in
like
maner
betwéen
the
howre
lines
.
It
will
also
procure
the
greater
Equator
,
which
wil
be
a
great
help
in
the
drawing
of
your
Dial
,
as
by
the
figure
following
you
may
perceiue
.
When
you
haue
thus
drawen
your
Diall
,
then
at
the
end
of
the
paper
wher
the
lines
be
of
greatest
distance
,
draw
the
line
I.
K.
parallel
to
the
Horizontall
line
,
make
likewise
the
other
line
L
M.
(
according
to
the
greatnes
of
your
plat
)
of
equall
distance
from
that
other
.
This
done
,
finde
out
(
or
rather
draw
a
line
vpon
your
plat
which
may
represent
)
the
true
Horizon
of
the
plat
:
cutting
the
paper
in
sunder
by
the
line
I.
K.
and
the
line
L.
M.
placing
it
vpon
your
plat
very
plain
,
so
that
one
of
the
edges
may
be
parallel
to
the
Horizon
.
Then
make
markes
vpon
the
plat
at
both
ends
of
all
the
howre
lines
drawing
by
those
marks
,
the
lines
for
the
howers
.
Draw
likewise
light
lines
vpon
the
plat
for
the
Stile
&
the
Substile
,
easily
to
be
extinguished
,
as
you
did
vpon
the
paper
.
Let
the
Stile
N.
be
fastened
ouer
the
Substile
as
you
haue
béen
taught
in
the
East
,
&
West
,
or
Equinoctiall
Dialls
.
But
here
note
,
that
the
Stile
must
not
be
of
equal
height
at
both
ends
.
But
let
it
be
so
high
,
as
the
distance
betwéene
the
Stile
&
the
Substile
is
in
the
place
where
it
standeth
:
as
in
the
examples
folowing
you
may
plainely
perceiue
.
A
North
Diall
.
Declining
Westward
|
65.
d.
|
Inclining
|
22.d.
20.ᵐ.
|
Distance
of
the
Meridian
from
the
horizon
|
50.d.
50.ᵐ.
|
Distance
of
the
Substile
and
the
Meridian
|
6.d.
35.ᵐ.
|
Distance
of
the
Stile
and
Substile
|
4.d.
15.ᵐ.
|
Eleuation
of
the
Pole
|
52.
d.
|
Hetherto
we
haue
taught
the
delineation
of
all
kindes
of
Dials
,
which
are
to
be
made
vpon
any
plaine
plat
or
superficies
:
now
followeth
the
garnishing
of
them
,
with
the
12.
Signes
,
and
the
howres
vnequall
.
dialing diagram
How
to
draw
the
12.
Signes
in
all
kindes
of
Dials
before
mentioned
.
CAP.
22.
FOr
somuch
as
sometime
the
12
signes
of
the
Zodiake
are
placed
in
Sunne
Dialls
,
know
in
what
signe
the
Sunne
is
at
any
time
(
which
albeit
any
kinde
will
receiue
,
yet
most
commonly
the
verticall
directly
opposite
to
the
South
are
garnished
therewith
.
)
Therefore
in
drawing
the
12.
Signes
,
in
these
South
,
and
all
other
kindes
of
Dialls
before
mentioned
,
doe
thus
.
Prepare
a
little
Table
of
Iron
,
Brasse
,
or
close
grained
wood
,
in
breadth
3.
or
4.
in
length
5.
or
6.
inches
.
Chose
for
the
Diameter
one
of
the
shortest
sides
,
wherein
draw
vpon
the
centre
A.
halfe
a
circle
to
be
deuided
into
two
quadrants
distinguished
with
a
line
drawen
from
the
centre
A.
to
the
arke
B.
parte
ech
quadrant
into
90.
degrées
.
The
line
A.
B.
is
héere
in
place
of
the
Equator
,
shewing
in
the
arke
the
beginning
of
Aries
and
Libra
.
Moreouer
how
to
finde
the
other
Signes
on
both
sides
,
séeke
in
the
Table
of
the
declination
of
the
Sunne
from
the
Equinoctial
circle
,
which
is
afterward
expressed
.
First
finde
out
the
degrées
of
the
distance
(
in
this
Table
)
of
the
beginning
of
Taurus
from
the
Equator
being
11.
degrées
30.
minutes
.
Account
this
distance
in
the
quadrant
from
the
letter
B.
towards
the
left
hand
,
and
at
the
end
of
this
number
draw
a
line
from
the
centre
A.
which
shall
shew
the
beginning
of
Taurus
and
Virgo
.
Account
like
wise
the
same
distance
on
the
other
side
from
the
line
A.
B.
and
make
a
line
for
the
beginning
of
Pisces
and
Scorpius
.
Againe
in
the
20.ᵈ.
12.ᵐ.
from
the
line
A.
B.
you
shal
haue
the
beginning
of
Gemeni
&
Leo
:
and
so
many
degrées
and
minutes
on
the
other
side
,
the
beginning
of
Aquarius
and
Sagittarius
.
To
conclude
on
both
sides
in
the
23
degrées
30
minutes
there
must
bée
on
the
one
part
Cancer
,
and
on
the
other
Capricorne
.
Afterward
draw
lines
from
the
centre
A
by
euery
marke
so
long
as
your
Table
will
receiue
▪
and
at
the
end
of
these
lines
let
the
caracters
of
the
12
signes
of
the
Zodiake
bée
fixed
:
as
in
the
figure
following
you
may
sée
.
dialing diagram
The
vse
of
this
Trigonall
instrument
in
writing
the
12
signes
in
Dialls
.
YOur
Diall
being
made
and
the
Stile
placed
therein
:
take
your
Trigonall
instrument
,
and
set
it
vpon
the
Stile
,
so
that
the
whole
Diameter
thereof
may
stand
plaine
vpon
the
edge
or
vpper
part
,
the
centre
A.
of
your
instrument
alwaies
remaining
in
one
place
of
the
Stile
.
Let
the
line
of
♋
bend
vpward
to
the
centre
of
your
diall
,
and
the
line
of
♑
downe
ward
.
Then
fasten
a
thred
at
the
vppermost
end
of
your
trigonal
in
euery
line
of
the
signes
,
so
that
you
may
direct
it
downward
by
the
centre
A.
to
the
plat
of
your
Diall
:
and
where
the
ende
of
the
thred
shall
touch
the
Diall
,
make
a
marke
.
Then
mouing
the
Trigonal
on
the
right
hand
,
so
that
the
thred
may
bée
stretched
on
the
left
hand
,
make
there
likewise
a
prick
vpon
the
plat
.
When
you
haue
thus
done
4
or
5
times
vpon
the
one
side
of
the
diall
:
(
that
is
on
the
left
hand
)
doe
so
likewise
on
the
other
side
on
the
right
hand
.
These
markes
being
thus
made
,
draw
(
with
your
compasses
or
rather
with
a
crooked
ruler
made
according
to
those
markes
)
a
line
by
them
.
Doe
thus
with
each
one
of
the
7
lines
of
your
Trigonal
.
When
you
haue
drawne
al
these
lines
,
(
being
crooked
,
except
the
middle
line
,
which
is
right
,
and
representeth
the
Equator
)
then
at
the
ends
of
them
write
the
caracters
of
the
12
signes
on
this
wise
.
First
on
the
right
hand
toward
the
East
,
at
the
ende
of
the
vpper
line
,
write
or
place
♑
.
At
the
second
line
downward
♒
.
At
the
third
♓
.
At
the
fourth
♈
.
At
the
fift
♉
at
the
sixt
♊
,
at
the
seuenth
♋
.
Then
on
the
other
side
on
the
left
hand
toward
the
West
,
at
the
ende
of
the
nethermost
line
place
♋
.
At
the
second
♌
,
at
the
third
♍
,
at
the
fourth
♎
,
at
the
fift
♏
,
at
the
sixt
♐
.
And
finally
againe
at
the
vppermost
set
♑
.
This
done
,
remember
that
in
what
place
of
the
Stile
the
centre
A.
of
your
Trigonall
was
placed
,
there
fasten
a
small
péece
of
yron
or
any
such
like
thing
,
which
may
shewe
with
the
shadowe
thereof
,
the
Signe
which
the
Sunne
shall
be
in
at
any
time
:
vnlesse
the
houre
lines
bée
so
short
,
that
where
the
small
péece
of
yron
should
be
placed
,
you
may
cut
the
Stile
that
the
ende
thereof
shall
shew
it
.
But
the
first
is
the
most
conuenient
way
for
the
vse
thereof
.
dialing diagram
You
may
in
like
manner
with
this
Instrument
drawe
or
place
the
12
signes
in
Horizontal
,
East
,
West
,
and
all
other
kindes
of
Dials
,
which
before
are
recited
:
because
the
difference
is
nothing
but
in
placing
the
12
signes
at
the
ends
of
the
lines
:
the
true
doing
where
of
,
you
may
easily
perceiue
by
the
course
of
the
Sunne
.
For
in
the
South
Erect
,
when
the
Sunne
occupieth
Cancer
,
then
is
the
line
of
♋
furthest
distant
from
the
centre
of
the
Diall
.
But
in
the
Horizontall
Diall
,
the
line
of
♋
is
next
to
the
centre
.
Few
words
shall
suffice
for
this
matter
:
experience
shall
easilie
teach
you
herein
.
How
to
place
the
vnequall
houres
in
a
Horizontall
Diall
.
CAP.
23.
FIrst
you
shall
vnderstand
,
that
by
an
vnequall
hower
is
ment
the
12
part
of
the
day
whether
it
be
short
or
long
.
For
when
the
Sunne
is
in
the
Equinoctiall
circle
,
the
day
hath
12
equall
,
and
like
wise
12
vnequall
houres
.
But
in
winter
solstice
,
when
the
dayes
be
at
the
shortest
,
and
containeth
with
vs
(
where
the
Pole
is
eleuated
aboue
the
Horizon
52
degrées
)
onely
7
houres
,
36
minutes
:
then
the
vnequall
houres
be
lesse
.
For
if
you
diuide
these
7
houres
36
minutes
by
fractions
into
12
:
you
shall
finde
onely
38
minutes
of
an
equall
houre
,
to
make
one
vnequall
houre
.
But
in
the
sommer
solstice
,
when
the
dayes
bée
at
the
longest
,
and
hath
16
houres
,
24
minutes
:
then
one
houre
with
24
minutes
maketh
one
houre
vnequall
.
These
bée
like
wise
called
the
houres
of
the
Planets
,
and
are
placed
in
Dialls
on
this
maner
.
Your
Diall
being
made
and
prepared
,
draw
vpon
it
the
12
signes
of
the
Zodiake
(
as
you
were
taught
before
)
so
large
as
your
plat
will
giue
leaue
,
&c.
Note
that
alwaies
the
Meridian
line
,
or
12
equall
houre
,
is
the
6
vnequall
houre
.
Marke
likewise
,
that
when
the
Sunne
entreth
into
the
beginning
of
♈
and
♎
,
both
the
equall
and
the
vnequall
houres
be
of
like
quantitie
.
For
the
7
equall
houre
in
the
morning
is
the
first
vnequall
,
and
the
8
equall
the
2
planetare
houre
,
&c.
But
in
the
Tropike
of
♋
it
is
otherwise
:
for
then
the
vnequall
houres
be
greater
then
the
equal
.
Therefore
account
how
many
houres
and
minutes
is
in
the
longest
day
for
your
Eleuation
,
changing
all
the
minutes
of
those
houres
into
one
totall
summe
.
Then
diuide
this
number
by
12
:
and
the
quotient
shall
shew
how
many
minutes
of
an
equall
maketh
one
vnequall
houre
.
Example
hereof
:
with
vs
the
longest
day
is
16
houres
24
minutes
.
Wherefore
I
multiplie
60
which
is
the
minutes
of
an
equal
houre
,
by
16
,
which
is
the
summe
of
houres
of
the
longest
day
,
and
the
product
ariseth
to
960
,
whereunto
I
adde
24
the
minutes
remayning
,
then
the
number
shall
be
984
,
which
being
diuided
by
12
,
the
quotient
is
82.
Wherefore
I
conclude
that
82
minutes
of
an
equall
,
maketh
one
vnequall
or
planetare
houre
.
Then
to
draw
them
in
Dialls
worke
thus
.
First
in
the
Tropike
of
♋
diuide
the
space
betwéene
each
houre
into
60
equall
partes
,
but
because
those
distances
bée
so
small
,
for
the
most
part
,
that
this
cannot
be
done
:
therefore
it
shall
suffice
to
diuide
euery
one
of
them
into
thrée
equall
partes
.
Then
shall
euery
parte
conteine
20ᵐ.
and
thrée
of
them
60ᵐ.
which
is
one
equall
houre
.
When
as
therefore
you
will
place
the
7
vnequall
houre
,
account
from
the
Meridian
line
,
or
12
houre
,
4
parts
and
2
minutes
(
which
is
82
minutes
)
and
make
there
a
marke
.
Then
place
your
ruler
by
this
point
or
marke
,
and
the
intersection
of
the
line
of
♈
and
♎
,
and
the
first
houre
after
noone
:
drawe
a
line
from
one
Tropike
to
another
,
that
is
from
♋
to
♑
.
Then
for
the
placing
of
the
8
vnequall
houre
,
account
from
the
7
last
made
,
4
of
the
foresaid
parts
and
two
minutes
make
there
a
marke
,
by
which
and
the
intersection
of
the
line
of
♈
and
♎
and
the
line
of
the
second
houre
after
noone
,
the
ruler
being
placed
,
draw
a
line
,
as
before
.
For
the
9
,
account
from
the
8
last
made
,
likewise
4
parts
and
two
minutes
,
drawing
a
line
as
before
.
Doe
in
like
maner
for
the
drawing
of
all
the
other
remaining
:
that
is
,
for
the
10
,
and
11.
The
12
being
the
Sunne
sitting
shall
néede
no
line
.
As
you
haue
finished
the
vnequall
houres
on
this
side
for
the
afternoone
,
doe
in
like
maner
for
those
in
the
forenoone
:
accounting
from
the
Meridian
4
parts
and
2ᵐ.
of
an
equall
houre
,
to
each
vnequall
,
drawing
,
as
before
,
lines
from
one
Tropike
to
another
.
You
may
place
the
figures
for
the
vnequall
or
planetare
houres
,
at
the
ende
of
the
lines
vnder
the
Tropike
of
Capricorne
,
or
aboue
the
line
of
Cancer
as
you
will
.
Note
that
the
same
part
of
the
Stile
which
sheweth
the
12
signes
,
shall
like
wise
shew
the
vnequall
houres
.
For
better
vnderstanding
hereof
:
Behold
the
Figure
following
.
An
Horizontall
Diall
.
dialing diagram
How
to
place
the
houres
vnequall
in
a
South
erect
direct
Diall
.
CAP.
24.
THere
is
almost
the
same
maner
of
placing
the
vnequall
houres
in
this
kind
,
as
in
the
Horizontall
,
differing
onely
herein
,
that
whereas
you
diuided
the
spaces
betwéene
the
houre
lines
,
in
the
Tropike
of
♋
,
(
which
is
next
to
the
centre
of
your
Diall
)
and
accounted
4
partes
2
minutes
of
an
equall
,
to
one
vnequall
houre
:
in
this
you
must
diuide
the
Tropike
of
♑
,
(
which
is
likewise
next
to
the
centre
of
the
Diall
)
taking
onely
2
partes
wanting
2
minutes
,
(
that
is
38m.
)
of
an
equall
houre
to
ech
vnequall
.
Therefore
your
Diall
being
prepared
,
and
the
12
signes
of
the
Zodiake
placed
therein
,
&c.
account
how
many
houres
and
minutes
be
in
the
shortest
day
in
your
country
,
changing
all
the
houres
into
minutes
(
giuing
to
each
houre
60
minutes
.
)
Diuide
the
product
by
12
,
and
the
quotient
shall
shew
how
many
minutes
of
an
equall
,
will
be
answerable
to
each
vnequall
houre
.
Example
,
the
shortest
day
with
vs
is
7
houres
,
36
minutes
,
which
being
multiplied
into
one
grosse
number
of
minutes
,
the
product
is
456
,
which
I
diuide
by
12
,
and
the
quotient
is
38.
Therefore
I
affirme
that
38
minutes
of
a
vulgar
or
equall
,
maketh
one
planetare
or
vnequall
houre
.
Then
diuide
the
Tropike
of
♑
here
,
as
in
the
Horizontall
you
did
the
Tropike
of
♋
.
Afterward
account
from
the
Meridian
line
38m.
(
or
2
parts
wanting
,
2m.
)
of
an
equall
houre
to
each
vnequall
,
&c.
Finish
all
thinges
else
in
this
Meridionall
erect
direct
,
as
you
were
taught
in
the
Horizontal
.
The
figure
ensueth
.
A
South
Diall
.
dialing diagram
The
placing
of
the
howres
vnequall
in
East
and
West
Dials
.
CAP.
25.
FIrst
draw
your
Diall
true
,
then
place
the
12
Signes
of
the
Zodiake
in
it
:
which
you
may
doe
on
this
wise
.
The
Stile
of
your
Dial
being
fixed
therin
,
as
before
hath
béen
taught
,
take
your
Trigonall
(
before
prescribed
)
and
place
it
vpon
the
edge
of
the
Stile
:
then
according
to
the
direction
of
the
thread
(
as
in
the
South
Diall
before
)
make
marks
vpon
the
plat
,
as
in
the
Figure
following
you
may
sée
.
Afterward
by
these
markes
draw
lines
as
before
you
did
,
placing
at
the
ends
of
them
the
Caracters
of
the
12
Signes
.
Moreouer
note
that
where
the
centre
A.
of
your
Trigonall
doth
touch
the
edge
of
the
Stile
,
there
fasten
a
small
péece
of
Iron
or
such
like
thing
,
which
may
shew
she
place
of
the
Sunne
in
euery
Signe
,
and
likewise
the
planetare
or
vnequall
howres
.
dialing diagram
When
as
therfore
you
would
place
the
howres
vnequal
in
those
kindes
of
Dialls
,
account
the
m●mber
of
howres
and
minutes
,
which
the
halfe
of
the
longest
day
in
your
Country
doth
conteine
.
Example
.
With
vs
the
longest
day
conteineth
16
howres
,
24ᵐ.
the
halfe
thereof
is
8
howres
12ᵐ.
wherefore
numbring
in
the
circumference
of
the
circle
from
A.
to
D.
6
howres
,
(
for
that
quadrant
conteineth
6
equall
howres
)
and
from
D.
toward
C.
the
other
2.
howres
and
12
minutes
,
so
that
you
may
haue
from
A.
by
D.
toward
C.
the
iust
halfe
of
the
longest
day
,
at
the
end
thereof
make
a
point
X.
Then
diuide
the
arke
A.
X.
into
6.
equall
partes
.
Afterward
placing
the
ruler
vpon
the
centre
E.
and
eche
one
of
these
partes
,
where
it
shall
touch
the
Contingent
line
D.
F.
make
marks
.
Likewise
in
the
other
line
of
Contingence
G.
B.
make
these
markes
,
being
of
equall
distance
in
this
line
from
the
point
B.
as
the
other
be
from
the
point
D.
Then
place
the
ruler
vpon
two
of
these
marks
(
being
equidistant
from
the
points
B.
D.
)
in
both
the
Contingent
lines
,
and
where
it
shal
touch
the
Tropike
of
♋
make
markes
.
This
done
,
lay
the
ruler
vpon
the
first
marke
in
the
Tropick
of
♋
next
vnto
X
,
and
the
intersection
of
the
line
of
the
6
hower
,
with
the
line
of
the
beginning
of
♈
and
♎
,
drawing
a
manifest
line
from
one
Tropike
to
another
,
which
(
if
you
haue
wrought
all
things
true
)
will
be
parallele
to
the
Horizon
,
and
it
shall
be
the
12.
vnequall
hower
line
in
the
West
Diall
,
and
the
Horizon
or
Sunne
rising
in
the
East
Diall
.
Againe
,
place
your
ruler
vpon
the
second
marke
in
the
Tropike
of
Cancer
,
and
the
intersection
of
the
line
of
the
5.
hower
with
the
Equator
,
or
line
of
Aries
and
Libra
,
drawing
like
wise
a
line
,
which
shall
shew
the
first
howre
in
the
East
,
and
the
11.
howre
in
the
West
Diall
,
make
on
this
wise
all
the
other
vnequall
howres
,
namely
the
10
,
9
,
8
,
and
7
,
in
the
West
Diall
.
And
the
2
,
3
,
4
,
5
,
in
the
East
Diall
.
dialing diagram
The
making
of
an
Horizontall
Sphericall
or
hollow
Diall
.
CAP.
26.
FIrst
prepare
your
Sphere
or
plat
perfectly
hollow
,
of
what
quantity
you
wil.
Then
with
your
compasses
diuide
the
vpper
brimme
thereof
,
into
4
equall
partes
,
marking
it
with
the
letters
A.
B.
C.
D.
Afterward
open
your
Compasses
to
the
widenes
of
one
Quadrant
,
either
A.
C.
or
A.
D.
and
with
that
widenesse
,
one
foote
being
placed
in
the
point
D.
draw
an
obscure
or
light
line
from
A.
to
B.
This
done
,
set
one
foote
of
your
Compasses
in
the
point
C
and
with
the
other
you
shall
try
whether
the
plat
be
perfectly
Sphericall
or
not
:
for
if
it
be
,
your
Compasses
will
fall
in
the
same
line
which
you
made
before
,
but
if
it
be
not
perfect
you
may
amend
it
.
And
then
draw
this
line
manifest
,
so
that
it
may
continue
.
For
it
shall
be
the
Meridian
line
,
shewing
the
12
howre
.
Againe
,
place
one
foote
in
the
point
A.
drawing
with
the
other
a
light
line
from
C.
to
D.
then
one
foote
being
set
in
B.
you
may
try
with
the
other
,
as
before
,
the
truth
of
the
line
last
made
.
Now
where
these
two
lines
cut
eche
other
in
the
bottome
of
the
plat
,
place
the
letter
E.
Then
diuiding
the
quadrant
A.
E.
into
90.ᵈ.
and
accounting
therein
the
Eleuation
of
the
Pole
from
E.
toward
A.
make
the
point
F.
by
which
the
arke
line
of
♈
and
♎
,
representing
the
equinoctiall
circle
,
shall
be
drawen
.
Afterward
séeke
out
the
greatest
declination
of
the
Sun
from
the
Equator
,
(
which
you
shall
finde
in
the
table
of
the
declination
of
the
Sunne
)
which
is
23.ᵈ.
30.ᵐ.
Then
account
23.ᵈ.
30.ᵐ.
from
F.
toward
E.
making
there
a
mark
for
the
arke
of
Cancer
.
Likewise
from
F.
toward
A.
number
the
same
distance
,
for
the
arke
line
of
Capricorne
.
This
done
,
account
from
F.
toward
E.
20.ᵈ.
12.ᵐ.
make
there
also
a
marke
for
the
line
of
♊
and
♌
.
And
the
like
space
from
F.
towards
A.
for
the
arke
of
♒
and
♐
.
To
conclude
,
number
from
F.
towards
E.
11.ᵈ.
30.ᵐ.
making
there
also
a
marke
for
the
●ine
of
♉
and
♍
:
and
so
much
from
F.
toward
A.
for
♓
and
♏
.
When
you
haue
thus
made
marks
for
al
the
arkes
of
the
12
Signes
,
open
your
compasses
to
the
Quadrant
of
the
Spheare
,
that
is
,
from
A.
to
C.
which
widenes
of
the
compasses
remaining
,
place
one
foote
in
the
point
F.
in
the
arke
of
♈
and
♎
in
the
Meridian
:
and
where
the
other
foot
shall
touch
the
same
Meridian
towards
B
make
the
point
G.
which
shall
represent
the
Pole
antartic●
,
by
which
as
it
were
from
a
centre
,
draw
a
line
from
the
point
D.
by
F.
to
C.
which
shall
be
the
line
of
Aries
and
Libra
.
Then
one
foote
of
your
compasses
remaining
in
the
point
G.
with
the
other
draw
lines
from
one
side
of
the
plat
to
the
other
,
by
euery
marke
before
made
for
the
12.
Signes
of
the
Zodiake
.
The
12.
Signes
being
thus
finished
,
procéede
to
the
diuision
of
the
equall
howres
on
this
manner
.
Diuide
the
arke
of
the
Equator
into
12.
equall
partes
,
beginning
at
D.
by
F.
ending
in
C.
Then
open
your
Compasses
to
the
quadrant
of
the
plat
,
and
the
same
widenesse
of
them
remaining
,
place
one
foote
on
the
first
point
of
the
diuision
next
C.
in
the
Equator
,
and
if
you
haue
diuided
the
Equator
equally
,
the
other
foote
will
touch
the
first
part
beyond
F.
towards
D.
by
which
from
the
centre
G
to
the
edge
of
the
plat
,
draw
a
line
,
which
shall
shew
the
first
howre
afternoone
.
This
done
,
remoue
your
compasses
(
that
widenesse
remaining
)
placing
one
foote
in
the
second
part
from
C.
towards
F.
and
the
other
foote
touching
the
second
part
from
F
towards
D.
make
a
line
as
before
,
from
the
centre
G.
to
the
brimme
of
the
plat
,
to
shew
the
2.
howre
afternoone
.
In
like
manner
,
finish
all
the
other
howre
lines
,
namely
the
3
,
4
,
5
,
6
7
,
8
,
for
the
afternoone
.
Then
doe
likewise
on
the
other
side
for
the
howres
in
the
forenoone
,
namely
the
11
,
10
,
9
,
8
,
7
,
6
,
5
,
and
4
drawing
lines
from
the
centre
G.
by
euery
diuision
,
to
the
brimme
of
the
plat
,
&c.
The
placing
of
the
vnequall
howres
in
this
Diall
.
When
you
will
place
the
howres
vnequal
in
this
Sphericall
Dial
,
diuide
the
Tropick
of
Cancer
and
of
Capricorne
ech
of
them
into
12.
equall
parts
,
as
before
you
did
the
Equator
for
the
equall
howres
.
Then
with
the
compasses
ioyne
eche
thrée
points
,
of
these
thrée
arkes
,
answerable
into
one
line
or
arke
,
vntill
you
haue
made
12.
lines
to
shewe
the
12.
vnequall
howres
,
as
in
the
figure
following
you
may
sée
.
Whereof
the
Meridian
,
or
12.
vnequall
howre
shall
alwaies
be
the
6.
vnequall
howre
.
In
placing
the
figures
to
the
equall
&
vnequall
howres
,
and
the
Caracters
to
the
12.
Signes
of
the
Zodiake
,
the
figure
may
sufficiently
shewe
,
notwithstanding
you
may
place
them
where
you
will
,
giuing
to
ech
signe
his
proper
Caracter
,
and
euery
howre
equall
and
vnequall
their
proper
figures
or
names
.
Fire
the
Stile
in
the
centre
G.
standing
vp
so
high
as
the
brimme
of
the
plat
,
so
that
the
vpper
end
may
appeare
as
the
centre
of
the
circumference
,
which
you
may
try
,
by
placing
a
ruler
vpon
the
points
A.
B.
And
againe
vpon
C.
D.
In
like
manner
you
may
examine
it
with
your
Compasses
,
but
the
former
,
as
practise
wil
teach
you
,
is
the
more
conuenient
way
.
You
may
,
if
you
wil
,
haue
the
Stile
stand
aboue
the
plat
,
so
that
it
may
shew
the
equall
howres
aboue
the
edge
of
the
Sphere
,
and
then
fasten
a
knot
of
equall
height
with
the
plat
,
which
shall
shew
the
motion
of
the
Sunne
in
the
12.
Signes
and
the
vnequall
houres
,
which
otherwise
the
end
of
the
Stile
should
doo
:
as
in
the
figure
following
you
may
perceiue
.
The
Figure
of
an
hollowe
Horizontall
Diall
.
dialing diagram
The
making
of
a
South
Spherical
erect
direct
Diall
.
CAP.
27.
YOu
shall
vnderstand
that
the
making
of
this
kind
differeth
almost
nothing
from
the
Horizontall
:
except
onely
in
the
accounting
the
beginning
of
the
Eleuation
of
the
Pole
,
&
drawing
the
houres
vnequall
.
First
your
Sphear
or
plat
being
prepared
,
and
parted
into
foure
Quadrants
,
as
before
in
the
Horizontall
you
were
taught
,
diuide
the
quadrant
E.
A.
into
90
degrees
.
Then
number
in
it
the
Eleuation
of
the
Pole
from
A.
toward
E.
marking
the
ende
of
the
number
with
F.
Afterward
open
your
compasses
to
the
quadrant
of
the
plat
,
and
the
one
foote
placed
in
F.
extend
the
other
in
the
Meridian
line
towards
B.
making
the
point
G.
where
it
shall
touch
the
Meridian
line
:
from
which
point
as
a
centre
you
shall
draw
the
lines
for
the
12
signes
,
as
you
were
taught
in
the
Horizontall
.
Diuide
likewise
,
and
draw
the
lines
for
the
equall
houres
,
as
before
in
the
Horizontall
.
The
placing
of
the
houres
vnequall
in
this
kinde
is
done
,
as
in
the
South
Erect
Direct
vpon
a
plaine
superficies
,
except
onely
that
whereas
there
you
did
draw
them
with
a
ruler
,
here
you
shall
doe
it
with
compasses
on
this
manner
.
Open
your
compasses
to
the
Quadrant
of
the
plat
,
that
is
,
from
A.
to
C.
accounsing
from
the
Meridian
in
the
Tropike
of
Capricorne
,
two
parts
wanting
two
minutes
of
an
equall
houre
,
making
there
a
marke
:
And
that
widenesse
of
your
compasses
remaining
,
draw
a
line
from
that
marke
made
in
the
Tropike
♑
,
by
the
intersection
of
the
line
of
Aries
and
Libra
,
&
the
line
of
the
first
houre
in
the
afternoone
,
vnto
the
Tropike
of
Cancer
.
Draw
all
the
other
lines
for
the
vnequall
houres
in
like
maner
,
as
in
the
figure
you
may
plainely
sée
,
Fixe
the
Stile
in
the
centre
G.
as
you
did
in
the
Horizontall
,
placing
the
figures
for
the
equall
and
vnequall
houres
,
and
the
caracters
to
the
12
signes
,
as
in
the
example
following
,
or
otherwise
as
you
will
.
dialing diagram
The
making
of
a
Diall
vpon
a
Quadrant
,
or
the
Table
described
in
the
beginning
of
the
Booke
.
CAP.
28.
IF
you
will
make
this
Diall
vppon
a
Quadrant
alone
,
prepare
and
diuide
it
altogether
like
one
of
the
Quadrants
of
the
table
,
whose
making
is
prescribed
in
the
first
Chapter
:
or
if
you
will
make
it
vpon
that
instrument
alreadie
prepared
,
worke
thus
.
Diuide
the
diameter
E.
D.
into
foure
equall
partes
;
then
leauing
out
the
fourth
part
next
E.
describe
vpon
the
middle
point
betwéene
C.
and
S.
an
obscure
halfe
circle
:
which
diuide
into
sixe
equall
parts
.
From
each
point
of
which
diuision
draw
light
lines
vnto
the
Semidiameter
D.
E.
touching
it
squire
wise
.
Then
draw
nigh
to
the
line
D.
E.
two
other
lines
parallele
thereto
:
which
with
the
crosse
lines
drawne
from
the
halfe
circle
may
make
12
vnequall
quadrangles
,
wherein
the
12
signes
of
the
Zodiake
may
be
figured
:
the
North
towards
D.
the
South
toward
S.
And
to
the
intent
you
may
proportionally
part
these
Quadrangles
into
fiue
or
ten
degrées
:
diuide
those
sixe
parts
of
the
halfe
circle
equally
into
so
many
degrées
.
Then
drawe
againe
from
those
diuisions
right
liues
to
the
Dimetient
D.
E.
squire-wise
,
as
before
.
This
done
vpon
the
point
E.
from
S.
that
is
to
say
,
from
the
end
of
♐
and
beginning
of
♑
,
drawe
an
arke
to
the
Semidiamer
D.
E.
which
shall
be
for
the
winter
Tropike
.
Againe
vpon
the
same
centre
,
draw
another
from
the
beginning
of
♈
and
♎
for
the
Equator
.
To
conclude
,
make
another
from
the
angle
D.
that
is
,
from
the
end
of
♊
and
beginning
of
♋
,
which
shall
bée
for
the
Summer
Tropike
.
By
the
helpe
of
these
arkes
,
you
shall
draw
the
houre
lines
,
so
that
you
first
know
the
height
of
the
Sunne
aboue
the
Horizon
,
at
euery
houre
,
when
it
occupieth
the
beginning
of
♑
,
♈
and
♋
.
Whose
altitude
is
thus
found
out
.
Take
the
Eleuation
of
the
Pole
,
and
the
Complement
thereof
:
also
the
declination
of
the
Sunne
from
the
Equinoctiall
,
and
the
distance
of
the
Sunne
from
the
Meridian
,
accounting
15
degrées
for
euery
houre
,
with
the
Complement
of
this
distance
.
Then
if
you
desire
to
knowe
the
altitude
of
the
Sunne
at
sixe
of
the
clock
either
in
the
morning
or
at
euening
(
at
which
houre
onely
in
Sommer
it
is
aboue
the
Horizon
)
multiply
the
Sine
of
the
Eleuation
of
the
Pole
,
by
the
Sine
of
the
declaration
of
the
Sunne
,
diuiding
the
product
by
the
whole
Sine
,
and
you
shall
haue
your
desire
.
But
if
the
Sunne
shall
bée
distant
from
the
Meridian
fewer
howers
then
sixe
,
multiply
the
Sine
of
this
distance
(
giuing
to
euery
houre
15
degrées
)
by
the
Sine
of
the
Complement
of
the
altitude
of
the
Pole
,
and
the
product
hereof
diuide
by
the
whole
Sine
.
Then
take
the
arke
of
the
quotient
from
90
degrées
,
and
the
first
number
found
out
shall
remaine
,
which
must
be
kept
.
Then
compare
the
Sine
of
this
number
found
out
,
with
the
Sine
of
the
Eleuation
of
the
Pole
,
augment
the
lesser
by
the
whole
Sine
,
diuiding
the
product
by
the
greater
:
Whereof
shall
come
a
quotient
Sine
,
to
the
complement
of
whose
arke
adde
the
declination
of
the
Sunne
,
if
it
shall
be
in
the
North
signes
,
or
subtract
it
from
that
,
if
it
occupieth
the
South
signes
.
And
if
the
number
which
commeth
hereof
shall
bée
greater
then
90
,
take
it
from
180
,
and
you
shall
haue
the
second
number
found
out
.
The
Sine
of
this
number
found
out
being
multiplied
,
by
the
Sine
of
the
first
number
found
out
,
shall
yéelde
a
product
,
which
part
by
the
whole
Sine
,
and
the
arke
of
the
quotient
Sine
shall
shew
the
desired
altitude
of
the
Sunne
for
the
houre
propounded
.
But
if
the
distance
of
the
Sunne
from
the
Meridian
shall
excéede
sixe
houres
(
that
is
90
degrées
)
take
the
degrées
of
that
distance
from
180
,
multiplying
the
Sine
of
the
remainder
by
the
Sine
of
the
Complement
of
the
altitude
of
the
Pole
,
diuiding
the
product
by
the
whole
Sine
,
and
subtract
the
arke
of
the
quotient
from
90
,
the
remainder
shal
be
called
the
First
number
found
out
.
The
Sine
of
which
number
found
out
compared
with
the
Sine
of
the
Eleuation
of
the
Pole
,
increase
the
lesser
by
the
whole
Sine
,
and
distribute
the
product
by
the
greater
.
Then
take
the
Complement
of
the
Declination
of
the
Sunne
,
from
the
arke
of
the
quotient
,
and
you
shall
haue
the
second
number
found
out
.
Finally
the
Sine
of
the
first
number
found
out
,
and
the
Sine
of
the
second
being
multiplied
by
themselues
,
and
the
product
parted
by
the
whole
Sine
;
the
quotient
Sine
shall
yéeld
an
arke
,
which
shall
bée
the
altitude
of
the
Sunne
.
But
when
the
Sunne
occupieth
the
beginning
of
♈
or
♎
you
shall
finde
the
altitude
thereof
euery
houre
,
onely
by
multiplying
the
Sine
of
the
Complement
of
the
distance
of
the
Sunne
from
the
Meridian
,
by
the
Sine
of
the
Complement
of
the
Eleuation
of
the
Pole
,
diuiding
the
product
by
the
whole
Sine
,
the
quotient
which
commeth
hereof
shall
yéeld
the
arke
of
your
desire
.
At
both
the
sixe
houres
,
because
the
one
sixe
is
the
rising
,
and
the
other
the
sitting
,
there
is
then
no
altitude
of
the
Sunne
aboue
the
Horizon
.
Moreouer
,
to
know
how
much
the
Meridian
altitude
is
,
of
the
Sunne
entring
into
♋
,
adde
the
greatest
Declination
thereof
,
to
the
Complement
of
the
Eleuation
of
the
Pole
:
and
by
subtracting
the
greatest
Declination
of
the
Sunne
,
from
the
complement
of
the
Eleuation
of
the
Pole
,
you
shall
likewise
haue
the
Meridian
altitude
of
the
Sunne
entring
into
♑
.
You
shall
likewise
séeke
the
height
of
the
Sunne
,
being
in
the
10
degrée
of
♉
aboue
the
Horizon
,
at
8
of
the
clock
before
noone
,
and
at
4
after
noone
:
at
7
in
the
morning
,
and
5
in
the
euening
:
at
both
6.
and
the
5.
houre
in
the
morning
,
and
7.
at
night
.
Also
at
5.
in
the
morning
and
7.
in
the
euening
,
the
Sunne
being
in
the
beginning
of
♊
.
But
because
the
working
of
this
,
to
finde
out
these
altitudes
,
requireth
much
time
and
labour
,
we
will
set
downe
these
distances
ready
found
out
,
calculated
for
the
Eleuation
of
the
Pole
50.ᵈ.
and
52ᵈ.
which
you
may
likewise
vse
without
any
notable
difference
,
where
the
Pole
is
Eleuated
49.ᵈ.
51.ᵐ.
and
53ᵈ.
The
first
table
calculated
for
50
degrees
.
Hour
.
|
Hour
.
|
♋
|
♈
♎
|
♑
|
10
deg.
♉
|
10
deg.
♊
|
|
|
D.
|
M.
|
D.
|
M.
|
D
|
M.
|
D.
|
M.
|
D.
|
M.
|
|
12
|
63
|
30
|
40
|
0
|
16
|
30
|
|
|
|
|
11
|
1
|
61
|
2
|
38
|
23
|
15
|
19
|
|
|
|
|
10
|
2
|
54
|
42
|
33
|
50
|
11
|
51
|
|
|
|
|
9
|
3
|
46
|
15
|
27
|
2
|
6
|
24
|
|
|
|
|
8
|
4
|
36
|
53
|
18
|
45
|
|
|
30
|
23
|
|
|
7
|
5
|
27
|
15
|
9
|
35
|
|
|
20
|
55
|
|
|
6
|
6
|
17
|
47
|
0
|
0
|
|
|
11
|
19
|
|
|
5
|
7
|
8
|
48
|
|
|
|
|
2
|
3
|
7
|
14
|
4
|
8
|
0
|
36
|
|
|
|
|
|
|
0
|
0
|
The
second
table
calculated
for
52
degrees
of
latitude
.
Hour
|
Hour
|
♋
|
♈
♎
|
♑
|
10
deg.
♉
|
10
deg
♊
|
|
|
D.
|
M.
|
D.
|
M.
|
D
|
M.
|
D.
|
M.
|
D.
|
M.
|
|
12
|
61
|
30
|
38
|
0
|
14
|
30
|
|
|
|
|
11
|
1
|
59
|
13
|
36
|
28
|
13
|
21
|
|
|
|
|
10
|
2
|
53
|
15
|
32
|
7
|
10
|
0
|
|
|
|
|
9
|
3
|
45
|
12
|
25
|
33
|
4
|
45
|
|
|
|
|
8
|
4
|
36
|
12
|
17
|
32
|
|
|
29
|
36
|
|
|
7
|
5
|
26
|
53
|
8
|
46
|
|
|
19
|
22
|
|
|
6
|
6
|
17
|
42
|
0
|
0
|
|
|
11
|
4
|
|
|
5
|
7
|
8
|
58
|
|
|
|
|
2
|
4
|
7
|
46
|
4
|
8
|
1
|
1
|
|
|
|
|
|
|
0
|
0
|
If
therefore
you
will
make
your
Quadrant
Horologicall
for
the
Eleuation
of
the
Pole
50.ᵈ.
extend
a
thread
,
or
lay
a
ruler
,
from
the
centre
E.
by
the
63.ᵈ.
30.ᵐ.
of
the
limbe
of
the
quadrant
,
beginning
at
F
and
where
the
thread
so
placed
shall
touch
the
Tropike
of
♋
,
there
make
a
point
or
marke
.
Againe
,
let
the
thread
be
placed
vpon
the
40.ᵈ.
of
the
limbe
,
and
where
it
shall
touch
the
Equator
,
there
also
make
a
marke
.
Thirdly
let
the
thread
be
drawen
by
the
16.ᵈ.
30.ᵐ.
of
the
quadrant
:
and
where
it
shall
touch
the
Tropike
of
♑
,
there
make
likewise
a
marke
.
This
done
,
search
out
the
centre
(
by
the
5.
Proposstion
4.
Euclid
)
and
ioyne
these
thrée
markes
into
one
arke
,
which
shall
be
the
line
for
the
12
hower
.
Afterward
place
the
thread
vpon
the
61.ᵈ.
2.ᵐ.
of
the
limbe
,
and
where
it
shall
cut
the
Tropike
of
♋
note
it
.
Draw
likewise
the
thread
vpon
the
38.ᵈ.
23.ᵐ.
of
the
limbe
,
marke
where
it
cutteth
the
Equator
.
Then
by
the
15.ᵈ
19.ᵐ.
of
the
limbe
extend
the
thread
,
making
a
marke
in
the
section
therof
and
the
Tropike
of
♑
.
Drawe
into
one
arke
these
thrée
markes
(
as
you
did
before
)
finding
out
the
common
centre
:
so
shall
you
haue
the
line
of
the
11.
hower
before
noone
,
and
1.
after
noone
.
In
like
maner
are
the
rest
of
the
hower
lines
drawen
by
3.
points
accounted
and
found
out
by
the
altitude
of
the
sunne
.
But
because
before
9.
and
after
3.
in
this
Eleuation
of
the
Pole
it
will
not
serue
for
this
delineation
,
there
must
another
be
made
by
the
table
of
the
12.
Signes
or
Quadrangles
.
Therfore
draw
that
from
the
10.ᵈ.
of
♉
,
so
shall
you
haue
a
line
or
place
wherein
the
third
points
may
be
marked
.
Then
to
prepare
the
points
of
the
arke
for
the
howers
of
8.
and
4.
of
7.
and
5.
and
both
the
6.
besides
the
two
markes
made
in
the
Tropike
of
♋
and
the
Equator
,
let
the
third
be
noted
in
the
arke
drawen
from
the
10.
degrée
of
♉
.
〈◊〉
draw
the
line
of
the
5.
and
7.
howers
,
vse
besides
the
Tropike
of
Cancer
and
this
drawen
from
the
10.
degrée
of
♉
,
the
third
which
shall
come
from
the
beginning
of
♊
.
The
line
of
4.
in
the
morning
,
and
8.
in
the
euening
is
very
short
,
included
in
the
angle
next
vnto
I.
Thus
you
haue
finished
9
arkes
or
lines
for
the
houres
,
of
which
each
one
of
them
doth
shew
two
houres
:
except
one
which
is
onely
for
the
●2
houre
.
And
to
the
intent
that
there
should
be
no
space
left
voyd
and
vnprofitable
betwéene
the
Tropike
of
♑
and
the
centre
E.
you
may
drawe
in
that
place
the
vnequall
houres
,
which
you
shall
very
easily
doe
on
this
maner
.
Describe
vpon
the
centre
E.
an
arke
very
little
distant
from
the
Tropike
of
♑
,
to
be
diuided
into
6
equall
parts
,
and
take
the
middle
point
betwéene
the
beginning
of
that
arke
at
S.
and
betwéene
E.
Then
vpon
this
point
▪
as
it
were
a
centre
,
make
a
halfe
circle
from
S.
to
E.
which
shall
be
the
line
of
the
6.
vnequall
hower
,
that
is
of
midday
.
Afterward
one
foote
of
the
compasses
being
placed
in
the
same
Semidiameter
E.
D.
and
remoued
eche
way
as
occasion
shall
require
:
and
the
other
extended
in
the
meane
time
so
far
that
it
may
touch
the
second
point
of
the
arke
diuided
into
6.
partes
,
and
the
centre
E.
draw
an
arke
or
line
from
the
centre
to
that
point
,
which
shal
shew
the
5.
and
7.
howers
.
Inlike
maner
are
the
other
4.
drawen
,
one
foote
of
the
compasses
being
remoued
,
as
necessity
shal
require
,
in
the
Semidiameter
E.
D
(
which
may
be
prolonged
if
it
shall
be
too
short
)
&
the
compasses
so
opened
,
that
the
other
foot
may
touch
the
point
of
the
diuided
arke
and
the
centre
E.
and
ioyne
them
all
into
one
arke
line
:
then
fixe
a
thread
in
the
centre
E.
well
waxed
,
hauing
two
small
beades
vpon
it
to
moue
with
a
plummet
of
iron
or
lead
.
Last
of
all
prepare
two
sights
of
brasse
or
other
metall
with
ioynts
,
which
you
must
place
in
one
right
line
vpon
the
side
or
edge
A.
B.
so
that
you
may
direct
them
,
and
againe
turne
them
downe
vpon
that
side
A.
B.
at
your
pleasure
:
that
(
if
you
make
this
Dial
vpon
the
Table
or
instrument
prescribed
in
the
beginning
of
this
book
)
they
be
no
hinderance
to
you
in
trying
or
examining
of
your
plats
.
Thus
is
your
diall
prepared
:
but
for
further
instruction
beholde
the
Figure
.
dialing diagram
The
vse
of
this
Diall
or
quadrant
Horologicall
.
TO
know
the
hower
of
the
day
when
the
Sun
shineth
,
worke
thus
.
First
séeke
out
in
some
Calender
in
what
Signe
and
degrée
the
Sun
is
at
that
day
:
then
extend
the
thread
with
the
beades
vpon
the
Semidiameter
E.
D.
and
place
the
neathermost
beade
vpon
that
degrée
,
in
the
Table
of
the
12.
Signes
,
which
the
Sunne
then
occupieth
.
Afterward
lifting
vp
your
quadrant
,
the
thread
with
the
plummet
hanging
at
liberty
,
let
the
Sun
beams
passe
thorow
both
the
sights
,
and
then
the
neathermost
bead
shall
shew
the
hower
of
the
day
either
before
,
or
after
noone
:
for
eche
line
as
you
see
,
hath
two
howers
,
but
you
may
easily
discern
what
hower
of
the
day
it
is
.
The
vnequall
hower
of
the
day
is
thus
found
out
.
The
neather
bead
being
placed
vpon
his
iust
degrée
in
the
Zodiake
,
lay
it
vpon
the
arke
of
the
12.
hower
,
the
thread
being
extended
:
thus
holding
this
immoueable
,
place
the
vppermost
bead
vpon
the
line
of
the
6.
hower
vnequal
.
This
done
the
Sun
beames
entring
both
the
sights
,
the
highest
bead
shal
shew
the
vnequall
,
and
the
neathermost
the
equall
hower
.
The
rising
and
sitting
of
the
Sunne
,
whereby
the
length
of
the
day
and
night
is
knowen
,
you
shall
finde
out
on
this
maner
.
Place
the
neather
bead
vpon
the
iust
degrée
of
the
Sunne
in
the
Zodiake
,
then
extend
the
thread
vpon
the
semidiameter
E.
F.
of
the
quadrant
,
and
the
bead
shall
shew
at
or
betwéen
what
howers
the
Sunne
riseth
and
falleth
.
The
height
of
the
Sunne
.
aboue
the
Horizon
at
any
time
of
the
day
is
thus
taken
.
Receiue
the
Sunne
beames
by
the
holes
in
your
sights
,
and
the
thread
with
the
plunmet
hauing
liberty
to
moue
,
shall
cut
in
the
limbe
of
the
Quadrant
the
iust
degrée
of
the
altitude
of
the
Sunne
aboue
the
Horizon
.
In
like
maner
is
the
Eleuation
of
the
Starres
aboue
the
Horizon
searched
out
.
You
shall
finde
out
the
eleuation
of
the
Pole
by
the
help
of
your
Quadrant
,
thus
.
Take
the
height
of
the
Sunne
at
12
of
the
clock
,
when
the
dayes
and
nights
bée
of
equall
length
,
which
being
subtracted
from
90ᵈ.
the
eleuation
remaineth
.
But
if
you
assay
that
vpon
any
other
day
then
the
Equinoct
.
you
must
consider
whether
the
Sunne
occupieth
the
North
,
or
the
South
signes
,
and
then
vse
the
table
of
the
Declination
of
the
Sunne
on
this
wise
.
When
the
Sunne
is
in
the
North
signes
,
substract
his
declination
from
the
Meridian
height
thereof
.
But
if
it
be
in
the
South
signes
adde
the
declination
to
his
Meridian
altitude
.
The
remainder
or
totall
summe
being
taken
from
90.ᵈ.
the
Eleuation
of
the
Pole
shall
remaine
.
How
to
make
an
instrument
,
whereby
you
may
know
the
iust
howre
of
the
night
by
the
Starres
.
CAP.
27.
FIrst
prepare
a
plat
or
Table
of
brasse
or
firme
and
solide
wood
,
which
will
not
change
or
bend
,
somwhat
thinne
,
let
the
forme
of
it
be
round
,
thrée
inches
broad
,
or
more
or
lesse
as
you
will
.
Draw
a
circle
nigh
vnto
the
edg
,
and
diuide
it
into
12.
equal
parts
:
wherein
shal
be
placed
the
12.
Signes
of
the
Zodiake
,
then
diuide
ech
of
these
parts
into
30.
equal
partes
,
which
shall
shew
the
number
of
the
daies
that
the
Sunne
moueth
in
euery
Sign
.
Make
a
second
circle
,
wherin
you
may
number
the
daies
,
and
a
third
circle
wherein
write
the
Caracters
of
the
12.
Signes
,
as
you
sée
in
the
Figure
following
.
Draw
likewise
another
circle
,
wherein
you
may
write
the
daies
of
euery
moneth
in
the
yéere
,
which
you
may
doe
by
any
Calender
,
but
for
more
easines
beholde
the
Table
following
,
whereby
you
may
likewise
doe
it
.
Month.
|
Daies
.
|
Deg.
|
M.
|
Caracters
of
the
12.
Signes
.
|
Signes
.
|
Ianuary
|
1
|
20
|
13
|
♑
|
Capricorne
.
|
|
15
|
5
|
33
|
♒
|
Aquarius
.
|
|
31
|
21
|
44
|
♒
|
|
February
|
14
|
5
|
52
|
♓
|
Pisces
.
|
|
28
|
19
|
48
|
♓
|
|
March
|
15
|
4
|
36
|
♈
|
Aries
.
|
|
31
|
20
|
18
|
♈
|
|
Aprill
|
15
|
4
|
51
|
♉
|
Taurus
.
|
|
30
|
19
|
13
|
♉
|
|
May
|
15
|
4
|
38
|
♊
|
Gemini
.
|
|
31
|
18
|
50
|
♊
|
|
Iune
|
15
|
3
|
3
|
♋
|
Cancer
.
|
|
30
|
17
|
22
|
♋
|
|
Iuly
|
15
|
1
|
40
|
♌
|
Leo.
|
|
31
|
16
|
58
|
♌
|
|
August
.
|
15
|
1
|
24
|
♍
|
Virgo
.
|
|
31
|
16
|
58
|
♍
|
|
September
|
15
|
1
|
40
|
♎
|
Libra
.
|
|
30
|
16
|
30
|
♎
|
|
October
|
15
|
1
|
30
|
♏
|
Scorpius
.
|
|
31
|
17
|
43
|
♏
|
|
Nouember
|
15
|
2
|
30
|
♐
|
Sagittarius
.
|
|
30
|
18
|
13
|
♐
|
|
December
.
|
15
|
3
|
38
|
♑
|
Capricorne
.
|
Enter
this
Table
,
and
you
shal
finde
that
the
first
day
of
January
must
be
placed
against
the
20.ᵈ.
13.ᵐ.
of
Capricorne
,
and
the
15.
day
against
the
5.ᵈ.
33.ᵐ.
of
Aquarius
,
&c.
Therfore
lay
your
ruler
vpon
the
centre
A.
of
your
plat
,
and
vpon
the
20.ᵈ.
13.ᵐ.
of
♑
,
and
where
it
shall
touch
the
circle
which
you
made
for
the
daies
of
euery
moneth
,
there
make
a
marke
which
shall
shew
the
first
day
of
January
.
Then
lay
it
vpon
the
5.ᵈ.
33.ᵐ.
of
♒
and
the
centre
A.
and
where
it
shall
touch
the
circle
,
make
a
marke
for
the
15.
day
of
January
.
Then
lay
your
ruler
vpon
A.
and
the
21.ᵈ.
44.ᵐ.
of
♒
,
and
make
likewise
a
marke
for
the
31.
day
of
January
.
Again
place
the
ruler
vpon
the
centre
A.
and
the
5.ᵈ.
52.ᵐ.
of
♓
,
for
the
14.
day
of
Februarie
:
worke
thus
with
all
the
rest
,
vntil
you
haue
set
down
the
beginning
and
middest
of
euery
month
,
as
the
Table
doth
direct
you
,
then
hauing
found
out
the
beginning
&
middest
of
euery
month
,
you
may
at
ease
diuide
euery
space
into
so
many
partes
,
as
there
be
daies
in
the
month
,
which
it
serueth
for
,
according
as
you
sée
in
this
figure
following
.
It
shall
be
also
necessary
to
make
one
circle
to
write
the
number
of
the
daies
of
the
moneth
,
and
another
for
the
names
of
the
monthes
:
you
must
make
also
a
hole
in
the
centre
of
this
plat
,
of
such
bignesse
,
as
you
may
sée
a
Starre
thorow
it
:
as
in
the
figure
you
may
perceiue
.
dialing diagram
Hauing
prepared
this
plat
with
the
circles
vpon
it
,
for
the
12.
Signes
and
months
,
you
must
prepare
an
other
whéele
full
of
téeth
,
which
you
shall
make
on
this
maner
.
Take
a
thime
Table
or
platte
of
the
same
matter
your
other
was
,
draw
a
circle
vpon
it
so
great
as
the
inward
circle
of
the
first
plat
,
and
diuide
it
into
24.
equall
parts
.
Then
draw
lines
from
the
centre
to
euery
one
of
those
parts
,
vntill
you
haue
so
many
as
there
be
howers
in
the
longest
night
in
your
Country
.
Then
cut
téeth
by
these
lines
for
the
howres
,
and
write
the
number
of
them
vpon
the
téeth
as
you
sée
in
this
figure
.
Let
the
tooth
for
the
12.
howre
be
so
long
from
the
centre
to
the
end
,
as
is
betwéen
the
centre
A.
of
the
other
plat
and
the
circle
of
the
12.
Signes
.
You
must
likewise
make
a
hole
in
the
centre
of
this
whéele
,
of
the
same
bignes
of
that
,
in
the
other
plat
.
The
thothed
wheele
.
dialing diagram
This
done
,
you
must
prepare
a
ruler
,
which
shal
be
placed
vpon
this
whéele
.
Take
therefore
a
thin
péece
of
wood
or
brasse
,
and
draw
vpon
it
a
light
line
:
at
y●
one
end
therof
in
the
middest
of
the
line
make
a
hole
of
the
same
bignesse
which
that
is
in
the
great
plat
and
tothed
whéele
.
Then
draw
a
circle
halfe
an
inch
wide
or
more
if
you
will
,
afterward
cut
the
ruler
round
at
the
end
,
cutting
off
likewise
the
one
halfe
of
the
breadth
of
the
ruler
by
the
line
.
Let
the
length
of
the
ruler
from
th●●●ntre
to
the
end
be
of
such
quantitie
,
as
is
from
the
centre
of
the
great
plat
to
the
outward
edge
,
and
an
inch
or
more
if
y
〈◊〉
〈◊〉
〈◊〉
.
dialing diagram
The
foreside
of
your
instrument
being
finished
:
the
backside
must
haue
two
small
holes
,
and
a
handle
,
which
may
turne
and
moue
about
.
Prepare
them
thus
.
Vpon
your
great
plat
on
the
backside
,
right
against
the
fourth
degrée
of
♍
,
nigh
the
edge
make
a
small
hole
,
wherein
the
little
pinne
of
the
handle
may
bée
pla●ed
,
when
néede
requireth
:
and
write
by
this
the
greater
Beare
.
Againe
,
right
against
the
28ᵈ.
1ᵐ.
of
♎
on
the
backside
make
another
hole
likewise
,
so
that
the
handle
being
:
remoued
to
it
,
the
pinne
may
enter
,
as
in
the
other
.
And
by
this
,
write
the
lesser
Beare
.
&c.
dialing diagram
Prepare
for
your
handle
a
thin
plate
of
yron
,
brasse
,
or
woode
,
about
sixe
inches
in
length
or
more
if
you
wil.
Draw
in
the
middest
of
it
a
line
:
at
the
one
ende
thereof
make
a
hole
in
the
middest
of
the
line
,
of
such
bignesse
as
the
hole
in
the
greater
plat
is
.
Vpon
this
handle
you
must
fasten
a
litle
short
pinne
right
in
the
line
,
so
that
the
handle
being
fastened
with
the
pinne
toward
the
backside
of
the
great
plat
,
and
being
moued
the
pinne
may
fall
directly
into
the
hole
.
Beholde
the
Figure
following
.
dialing diagram
Prepare
a
hollow
pinne
of
yron
or
brasse
,
according
to
this
figure
aboue
,
so
great
as
it
may
easilie
enter
into
the
hole
of
the
handle
,
so
that
it
may
turne
vpon
it
:
but
let
it
goe
close
into
the
great
plat
,
that
it
may
remaine
immoueable
.
Let
the
Tothed
whéele
and
the
ruler
moue
likewise
vpon
it
.
Then
place
the
Tothed
whéele
and
the
ruler
on
the
former
side
of
the
plat
vpon
the
pinne
,
and
on
the
backside
the
handle
with
the
little
pinne
towards
the
back
of
the
plat
:
fasten
them
so
together
,
that
the
handle
,
the
Tothed
whéele
,
and
the
ruler
may
turne
vpon
the
plat
seuerally
,
or
each
by
themselues
at
your
pleasure
,
and
as
néede
shall
require
.
Notwithstanding
you
must
bée
carefull
,
that
the
hole
in
your
pinne
may
bée
so
great
,
as
you
may
perfectly
sée
the
North
Starre
in
the
night
thorow
it
.
Then
your
instrument
shall
bée
finished
,
whose
vse
followeth
afterward
.
For
better
instruction
beholde
the
figure
.
dialing diagram
The
vse
of
this
instrument
.
FIrst
it
shall
bée
expedient
to
finde
out
the
Starres
seruing
to
this
purpose
,
which
you
may
doe
by
the
figure
following
.
dialing diagram
You
sée
in
this
figure
the
starres
which
serue
to
our
vse
.
The
Polare
Starre
is
a
bright
Starre
in
the
North
,
placed
in
the
tayle
of
the
lesser
beare
,
and
mooueth
but
a
small
course
,
as
in
the
figure
the
letter
A.
sheweth
.
There
is
also
another
Starre
of
the
lesser
beare
greater
and
brighter
then
the
other
,
and
is
noted
with
the
letter
B.
and
serueth
to
this
purpose
also
.
There
is
likewise
in
the
greater
beare
called
also
Charles
waine
,
and
of
countrie
men
the
plough
,
two
great
bright
starres
,
and
are
placed
almost
in
a
right
line
with
the
Polare
Starre
;
&
are
noted
with
the
letters
C.
D.
And
these
two
Starres
haue
5
other
bright
Starres
by
them
,
but
not
so
great
as
the
other
be
.
These
Starres
which
you
sée
in
the
figure
,
as
al
other
,
mooue
equally
aboue
the
Pole
,
and
finish
their
course
in
24
houres
.
Therefore
when
you
would
know
the
houre
of
the
night
by
this
instrument
,
do
thus
.
Place
the
right
line
of
the
long
tooth
of
the
12
houre
directly
ouer
the
day
of
the
moneth
,
and
turne
the
handle
on
the
backside
to
the
hole
of
the
greater
beare
,
and
your
instrument
shall
be
prepared
.
Then
lift
vp
your
instrument
by
the
handle
perpendicularly
,
so
that
it
declineth
on
neither
sides
:
and
beholding
the
Polare
Starre
thorow
the
hole
in
the
centre
,
moue
the
ruler
aboue
,
vntill
the
right
line
there
of
be
directly
against
,
or
séemeth
to
touch
the
two
Starres
of
the
greater
beare
,
and
vnder
the
line
you
shall
haue
the
iust
houre
of
the
night
:
which
you
may
finde
out
by
the
number
of
the
téeth
with
your
finger
in
the
night
.
But
if
you
cannot
sée
the
two
Starres
of
the
greater
beare
because
of
clouds
:
and
yet
you
may
sée
the
Polare
Starre
,
and
the
Starre
of
the
lesser
beare
,
noted
with
the
letter
B.
remoue
the
handle
on
the
backside
to
the
hole
of
the
lesser
beare
.
Then
lift
vp
your
instrument
as
before
,
and
beholde
the
Polare
Starre
at
the
hole
,
and
turne
the
ruler
to
the
foresaid
Starre
of
the
lesser
beare
,
and
you
shall
finde
the
true
houre
of
the
night
,
as
before
is
taught
.
The
making
of
a
Diall
,
to
knowe
the
houre
by
the
Moone
.
CAP.
30.
PRepare
a
square
péece
of
wood
or
metall
3
or
4
inches
ouer
,
draw
thereon
a
circle
so
great
as
you
can
,
draw
also
another
within
that
.
Now
because
the
Moone
finisheth
her
course
in
29
dayes
,
12
houres
,
and
44
minutes
,
part
the
inward
into
30
parts
in
this
maner
;
let
29
be
equally
diuided
,
and
the
30
which
is
the
last
must
not
be
so
great
by
a
third
part
:
wherefore
diuide
one
of
those
29
equall
parts
into
thrée
parts
,
and
take
two
of
them
for
the
30
and
last
part
.
dialing diagram
Cut
out
that
which
is
within
the
inward
limb
,
and
prepare
another
of
the
same
or
like
wood
or
metall
somewhat
thicker
,
and
worke
it
so
that
it
may
goe
into
the
former
so
much
of
the
thicknes
as
it
may
be
equal
on
the
backside
,
and
that
which
remaineth
of
the
thicknes
,
let
it
hang
ouer
the
foreside
of
the
first
plate
to
kéepe
it
from
falling
through
:
draw
a
circle
vpon
it
,
and
diuide
it
into
24
equall
parts
:
draw
from
these
parts
houre
lines
so
many
as
shall
suffice
for
the
longest
night
:
cut
that
which
ouerhangeth
with
téeth
at
euery
houre
,
but
especially
at
the
12
houre
make
a
long
tooth
,
fixe
a
wier
in
the
centre
for
the
Stile
equally
distant
from
the
circle
on
each
side
.
Let
the
Stile
hang
so
much
beneath
the
plat
,
as
it
is
aboue
,
because
you
shall
haue
as
much
vse
on
the
backside
as
before
.
dialing diagram
Cut
out
all
that
which
is
within
the
inward
circle
,
except
a
little
portion
to
support
the
Stile
,
so
that
this
shall
bée
but
as
a
hoope
.
Drawe
the
houre
lines
on
the
backside
of
this
plat
,
as
on
the
foreside
,
so
that
the
one
may
be
right
against
another
:
then
drawe
lines
on
the
inside
from
euery
one
of
these
lines
on
the
foreside
to
the
lines
on
the
backside
.
This
plat
or
whéele
must
be
moueable
and
turne
within
the
former
.
dialing diagram
The
vse
of
this
Diall
.
PLace
this
Diall
that
each
side
may
beholde
one
quarter
of
the
world
precisely
:
the
South
side
the
South
,
the
North
side
the
North
,
&c.
Moreouer
,
it
must
recline
according
to
the
eleuation
of
the
Equinoctiall
,
so
that
the
Moone
being
in
the
Equinoctiall
circle
,
shall
giue
light
both
aboue
and
beneath
this
Diall
.
You
may
place
it
perfectly
with
your
instrument
.
Your
Diall
being
thus
placed
,
when
you
would
knowe
the
houre
of
the
night
,
first
learne
the
age
of
the
Moone
by
an
almanack
,
and
especially
the
houre
of
the
change
,
then
turne
the
great
ouer-hanging
tooth
,
to
the
day
of
the
Moone
on
the
first
limb
,
and
to
the
houre
of
the
change
,
accounting
from
12
of
the
clock
.
The
shadow
of
the
Stile
shall
shew
the
howre
of
the
night
either
beneath
your
Diall
or
els
aboue
.
This
Diall
will
serue
also
for
the
Sunne
,
if
you
turne
the
great
tooth
of
the
moueable
whéele
to
the
little
strick
A.
which
is
right
opposite
to
the
beginning
of
the
first
,
and
end
of
the
last
day
of
the
Moone
,
nere
the
15.
day
,
and
then
it
is
fit
for
the
Sunne
.
For
it
differeth
nothing
from
the
North
reclining
direct
,
where
the
Reclination
is
equal
to
the
Eleuation
of
the
Pole
.
The
vse
of
the
Table
of
the
declination
of
the
Sunne
.
TAke
what
degrée
you
wil
of
any
signe
,
and
by
this
table
you
may
know
his
declination
from
the
Equinoctiall
circle
.
The
Signes
are
written
partely
on
the
head
of
the
Table
,
and
partely
on
the
foote
of
the
same
.
The
Degrées
in
the
first
columne
doe
serue
for
the
Signes
that
be
on
the
head
of
the
Table
,
and
the
Degrées
in
the
last
columne
doe
serue
for
the
Signes
in
the
foote
of
the
Table
.
And
the
common
Area
or
angle
against
the
Signe
and
the
Degrée
which
you
séeke
for
,
doth
containe
the
Degrées
and
Minutes
of
the
Declination
due
to
the
same
.
Example
.
I
would
know
how
much
the
tenth
degrée
of
Leo
doth
decline
from
the
Equinoctiall
:
I
must
looke
in
the
columne
ouer
Leo
,
right
against
the
number
of
10.
in
the
last
columne
,
where
I
finde
17.ᵈ.
46.ᵐ.
the
declination
therof
,
&c.
The
table
of
the
declination
of
the
Sunne
,
from
the
Equinoctial
circle
.
|
Aries
.
Libra
.
|
Taurus
.
Scorpius
.
|
Gemin●
.
Sagittarius
.
|
|
Deg.
|
Deg.
|
M.
|
Deg.
|
M.
|
Deg.
|
M.
|
Deg.
|
1
|
0
|
24
|
11
|
30
|
20
|
12
|
29
|
2
|
0
|
48
|
12
|
11
|
20
|
35
|
28
|
3
|
1
|
12
|
12
|
32
|
20
|
47
|
27
|
4
|
1
|
36
|
12
|
52
|
20
|
58
|
26
|
5
|
1
|
59
|
13
|
12
|
21
|
9
|
25
|
6
|
2
|
23
|
13
|
32
|
21
|
20
|
24
|
7
|
2
|
47
|
13
|
52
|
21
|
30
|
23
|
8
|
3
|
11
|
14
|
12
|
21
|
40
|
22
|
9
|
3
|
34
|
14
|
31
|
21
|
49
|
21
|
10
|
3
|
58
|
14
|
50
|
21
|
58
|
20
|
11
|
4
|
21
|
15
|
9
|
22
|
7
|
19
|
12
|
4
|
45
|
15
|
27
|
22
|
15
|
18
|
13
|
5
|
8
|
15
|
55
|
22
|
23
|
17
|
14
|
5
|
32
|
16
|
3
|
22
|
30
|
16
|
15
|
5
|
55
|
16
|
21
|
22
|
37
|
15
|
16
|
6
|
18
|
16
|
39
|
22
|
44
|
14
|
17
|
6
|
41
|
16
|
56
|
22
|
50
|
13
|
18
|
7
|
4
|
17
|
13
|
22
|
55
|
12
|
19
|
7
|
27
|
17
|
29
|
23
|
1
|
11
|
20
|
7
|
50
|
17
|
46
|
23
|
5
|
10
|
21
|
8
|
12
|
18
|
2
|
23
|
10
|
9
|
22
|
8
|
35
|
18
|
17
|
23
|
13
|
8
|
23
|
8
|
57
|
18
|
33
|
23
|
17
|
7
|
24
|
9
|
19
|
18
|
48
|
23
|
20
|
6
|
25
|
9
|
41
|
19
|
2
|
23
|
22
|
5
|
26
|
10
|
3
|
19
|
17
|
23
|
24
|
4
|
27
|
10
|
25
|
19
|
31
|
23
|
26
|
3
|
28
|
10
|
47
|
19
|
44
|
23
|
28
|
2
|
29
|
11
|
8
|
19
|
58
|
23
|
29
|
1
|
30
|
11
|
29
|
20
|
12
|
23
|
30
|
0
|
Deg.
|
Deg.
|
M.
|
Deg.
|
M.
|
Deg.
|
M.
|
Deg.
|
|
Virgo
.
Pisces
.
|
|
Leo.
Aquarius
.
|
|
Cancer
Capricorne
.
|
|
|
The
Table
of
Sines
.
The
whole
Sine
conteineth
100000.
partes
.
The
vse
of
the
Table
of
Sines
.
WHereas
the
making
of
some
Dials
,
and
this
Table
of
Sines
may
séeme
obscure
and
hard
to
them
who
are
not
acquainted
with
Sinicall
computation
,
it
shal
be
expedient
to
declare
the
vse
hereof
,
so
much
as
perteineth
to
the
vnderstanding
of
this
booke
,
omitting
all
other
vses
as
impertinent
to
our
present
purpose
.
Wherfore
know
that
the
Grades
or
Degrées
are
found
in
the
vpper
head
of
this
Table
,
and
the
Minutes
pertaining
to
the
Degrées
on
the
left
side
,
&
in
the
Area
or
common
méeting
of
them
both
,
a
number
which
is
called
the
Sine
,
answerable
to
ech
Degrée
and
Minute
,
offereth
it selfe
.
Againe
the
Sine
being
found
out
,
you
may
easily
know
the
arke
,
that
is
,
the
Degrée
and
Minutes
thereof
,
these
being
on
the
left
hand
,
the
other
on
the
head
or
vpper
part
.
Vnderstand
by
the
Complement
that
which
remaineth
of
any
number
being
taken
or
substracted
from
90.
Degrées
.
If
at
any
time
you
enter
the
Table
with
iust
Degrées
without
any
Minutes
,
resolue
one
Degrée
into
60.
Minutes
,
and
then
séeke
out
his
Sine
.
And
whereas
you
shall
finde
some
numbers
imperfect
,
you
must
remember
to
supply
their
want
with
those
which
be
perfect
immediatly
going
before
.
Example
.
The
Eleuation
of
the
Pole
at
Cambr.
is
52.
Degrées
,
whose
Sine
I
desire
to
know
,
therefore
resoluing
one
of
the
Degrées
into
Minutes
,
I
enter
the
Table
with
51.
degrées
,
60.
Minutes
,
and
in
the
common
Area
I
finde
the
Sine
to
be
78801.
If
then
you
desire
to
know
the
complement
of
this
Eleuation
,
substract
52.
out
of
90.
and
the
remainder
shal
be
38.
the
complement
thereof
,
and
entring
the
Table
with
37.ᵈ.
60.ᵐ.
you
shall
finde
in
the
Area
66.
which
number
because
it
is
imperfect
,
you
must
supply
the
want
thereof
by
adding
the
3.
former
figures
in
that
which
is
next
before
perfect
,
to
wit
,
615.
and
then
the
whole
number
shal
be
61566.
the
Sine
of
38.ᵈ.
which
is
the
Complement
of
52.ᵈ.
the
Eleuation
of
the
Pole
.
These
thinges
well
considered
,
there
is
nothing
in
the
booke
so
obscure
,
but
it
shall
séeme
plaine
and
easie
.
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
.
FINIS
.
Note
that
some
of
the
letters
in
the
Instrument
page
2.
are
omitted
in
the
printing
:
place
A.
at
the
vppermost
corner
towards
the
left
hand
,
B.
at
the
neathermost
,
C.
by
90.
beneath
,
and
D.
at
90.
aboue
.